Ignatius of Antioch Readings

 I offer this - with which I don't entirely agree:

The chief authorities for the history of the development of the episcopal idea are the writings, also pseudonymous, which have come down under the names of Clement of Rome and Ignatius the bishop of Antioch. Their coincidence in this point is the more remarkable, since the two represent quite different tendencies. Ignatius is a decided Paulinist, while Clement, in the name of his apostle, Peter, acknowledges the strictest Judaism. While they warn against heresies and schisms, and exhibit their danger, they insist no less emphatically on the importance of the episcopate as the Church’s sovereign power, representing God and Christ. The fundamental thought which animates both writers alike is, that neither for the individual, nor for the aggregate, is there any salvation but in the unity which ascends to the bishop, to Christ, and to God; that as soon as this union is abandoned, the Christian society is exposed to all the dangers of false doctrine and sin, of the most melancholy division and dismemberment.
Agreement with the bishop is the ever-recurring, the most urgent admonition of the pseudo-Ignatius. Christians must hold to the bishop alone, and do nothing without him, as the Lord did nothing without the Father, but everything in unity with him. If we are subject to the bishop, as Christ was to the Father, then we live not after the manner of men, but after the manner of Christ, who died for us, that in belief in his death we might escape death. The command of the Spirit is to do nothing without the bishop, to love union, to flee from schisms, to imitate Christ, as Christ imitates the Father. Especially, no ecclesiastical event may take place without the bishop. The eucharist is not to be deemed duly and validly performed, unless performed by him, or with his sanction. Where the bishop is, there the congregation is, as the Catholic Church is where Christ is. It is not allowed to baptise or to hold an agape without the bishop: only what he approves is pleasing to God; only so can whatever is done be done surely and validly. He who honours the bishop is honoured by God; he that does anything without the knowledge of the bishop serves the devil. He who belongs to God and Christ is also with the bishop. The happiness of those cannot be too highly esteemed, who are as entirely one with the bishop as the Church is one with Christ, and Christ with the Father, to the end that all may accord in unity. He who is not within the altar lacks the bread of God. If the prayer of one or two can avail so much, how much more that of the bishop and the whole congregation? Therefore the bishop may not be resisted; to be subject to God, we must look to the bishop as to the Lord himself, and honour him, as we honour Christ the Son of the Father.2 The bishop is therefore even called the substitute of God, the προκαθημένος εἰς τόπον Θεοῦ; he that hearkens to him hearkens not to him, but to the Father of Jesus Christ, as the ἐπίσκοπος πάντων. He that deceives the bishop deceives not him who is visible, but deceives the Invisible. The visible bishop is in the flesh (ἐν σαρκὶ ἐπίσκοπος), in bodily and material fashion, what God or Christ is in invisible spiritual fashion. The fundamental idea of the passages relating to the episcopate may therefore be correctly defined thus: “The bishops are essentially the representatives and organs of the unity of the Church, inasmuch as it belongs to the specific character of the episcopate, that they are the immediate representatives, empowered delegates, and organs of God and Christ. In them Christ has, so to speak, multiplied himself; in them he has given himself within the compass of Christendom a universal presence which can be apprehended by the senses. In all the congregations it is he who acts and guides the vital movement through his organ the bishop. Thus in reality it is one and the same person who is at the head of each separate congregation, although his representatives and organs are individually different. And thus all the congregations are joined together in the most intimate and pervading unity, while the condition of that unity is, that there be an organic connection between each community and its bishop.”
The same fundamental view of a system of ecclesiastical constitution based on the episcopate is contained in the pseudo-Clementine writings.

Ferdinand Christian Baur, The Church History of the First Three Centuries, trans. Allan Menzies, Third Edition, vol. 2, Theological Translation Fund Library (London; Edinburgh: Williams and Norgate, 1879), 31–34.

or if you prefer

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Some of that ministry had a significant itinerant dimension, beginning with the Gospels, continuing in Paul, and persisting in the late first-century Didache (Lk 9:1–6; 10:1–20; Acts 8:4; Rom 15:19; Did. 11–13). Itinerancy played a vital role in the spread of the gospel. What, however, was the relationship of itinerants to a church they visited, seeking to provide direction to and gain support from that church? What authority did prophets have in relation to formally appointed leaders? For a couple of centuries the church struggled with the relationship between institutional and charismatic ministry.
By the time of Constantine the answer was pretty clear: the church was the institutional church, though sometimes supplemented by other, self-authenticating ministry. That ministry was clearly subject, however, to the institutional church. For example, the rise of monasticism initially took place outside and away from the institutional church. When, however, monasticism was drawn into the church, its looser and more spontaneous qualities became very much subject to church direction. Holy men and women were welcome additional guests to the church banquet, but they could not upset the meal.
These changes occurred in the context of an increasingly hierarchical church structure. As early as the second century the need for institutionally identified authority figures was recognized. Without such development the church would splinter, relationally and doctrinally. Institutional containers were needed for the heady wine of the Spirit. “Do nothing without the bishop,” was the cry of Bishop Ignatius at the start of the second century. The aggressive promotion of this claim suggests that it was a contested matter; Ignatius was advancing into disputed territory. A century and a half later, the matter was not in dispute, at least not in the mainstream of church life. Cyprian viewed the bishop as the center of a church life that was united and held together by the mutual cohesion of its bishops.28 Bishops embodied the church: “You ought to know that the bishop is in the church and the church in the bishop; and if anyone be not with the bishop that he is not in the church.”

Laurie Guy, Introducing Early Christianity: A Topical Survey of Its Life, Beliefs Practices (Downers Grove, IL: InterVarsity Press, 2004), 21.

Or if you prefer commentary to history

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(b) Yet obedience to the bishop is of such decisive importance to Ignatius that he goes on virtually to define being Christian in terms of it. In this connection he appeals to the contrast between empty talk and actual deeds that he elaborates more fully in Eph. 14.2–15.2 (note especially the close parallel in Eph. 15.1). Some acknowledge the bishop but “do” everything (probably in matters of worship; cf. Mag. 7.1; Tr. 7.2; Phd. 4) “without him.” Here the contrast between words and deeds has been fused with another recurring theme in Ignatius: the call to do nothing without the bishop. In this connection Ignatius alternates between using ἄνευ “without” (Mag. 7.1; Tr. 2.2; Pol. 4.1) and χωρίς “without” (Tr. 7.2; Phd. 7.2; Sm. 8.2). Especially important is Pol. 4.1, where the expression “without (ἄνευ) your approval” (or “purpose”) points to secular contexts in which authority (especially political and administrative) is asserted. For here one is frequently commanded to do nothing without (or without the permission of) those in charge. The use of such language strengthens the impression left by Ignatius in our passage that he chose to define episcopal authority more strictly than others. At the same time, the appeal to secular models suggests that he did not (as Bauer thought) seek to reinforce discipline as the leader of a minority precipitating a split. Groups within the churches known to Ignatius are just beginning to become conscious of distinct aims (and, in some instances, distinct theologies) which lead to separation (see on Phd. 7.2; 11.1; Sm. 5.2; 8.2). Ignatius does define situations more sharply in administrative and theological terms, but apparently the majority were prepared to follow (see Introduction, 3.3); and it is from the standpoint of the dominant group that the bishop speaks when he labels the separate meetings of others as “invalid” (cf. Sm. 8.2). When he also says that the separatists do not meet “in accordance with the commandment,” it is unlikely that he is referring to any definite pronouncement (such as Matt 18:17*). “Commandment” is as broad a term in Ignatius (cf. Eph. 9.2; Tr. 3.1 v.l.; 13.2; Rom. inscr; Phd. 1.2; Sm. 8.1) as it is in the Johannine writings (see 2 John 6* for the expression “according to his commandments”). What Ignatius probably has in mind is the principle of love and unity inherent in the very fabric of the life of the church as he has come to understand it (note Heb 10:25* which also criticizes the failure to meet together, “as the manner of some is,” on general theological grounds). Thus Ignatius’ definition of Christianity in terms of obedience to the bishop is not without its deeper ground.

William R. Schoedel, Saint Ignatius Bishop of Antioch, and Helmut Koester, Ignatius of Antioch: A Commentary on the Letters of Ignatius of Antioch, Hermeneia—a Critical and Historical Commentary on the Bible (Philadelphia: Fortress Press, 1985), 109–110.

Or from a dictionary entry on unity:

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D. Ignatius of Antioch
The trajectories of Church unity arising from Paul and John are further developed outside the NT in Ignatius, in whom unity is of the greatest significance. Negatively, sin for Ignatius was basically division (Phild. 2.1). It was that lack of unity which made humanity so vulnerable to the forces of evil. Unity, then, was the supreme gift (Magn. 1.2; 15). It is through Jesus Christ that unity is obtained; it is only unity with and in him that produces true harmony among people. Thus unity is possible only within the Church and is in fact promised by God (Trall. 11.2). It is for that reason that Ignatius so strenuously urged unity with and obedience to the bishop: “Be united with the bishop and with those who preside, for an example and lesson of imperishability” (Magn. 6.2; cf. Ign. Eph. 4; Phild. 3.2). Or, in Johannine terms, “As, then, the Lord did nothing apart from the Father, either by himself or through the apostles, since he was united with him, so you must do nothing apart from the bishop and the presbyters” (Magn. 7.1; cf. Phild. 7.2, Eph. 5.1–2, Mag. 13.1–2, Tr. 7.2.) It is the bishop who guarantees the true unity of the Church (Smyrn. 8.2), becoming virtually identified with Christ as the guarantor of unity (Trall. 2.1, Eph. 6.1, Smyrn. 9.1). So, too, the ministry of Ignatius has been devoted to unity (Phild. 8.1). Finally, as in Paul but developed even further, the Eucharist is the sacrament of unity. There is one flesh of Christ and one Eucharist. Therefore, the Church, too, is to be one (Eph. 20.2; Phild. 3–4; Smyrn. 1.2, 7.1).

Walter F. Jr. Taylor, “Unity/Unity of Humanity,” in The Anchor Yale Bible Dictionary, ed. David Noel Freedman (New York: Doubleday, 1992), 752–753.

Does Ignatius or another church father define a bishop or outline the tasks of this particular office?

The Bible and the Didache provide this information.

How can Logos help me find this biblical and Didache text?

The quotation given provides the Bible and Didache references. Just look them up. If you don't have a book with Didache in the title do a milestone search on the reference as the Didache is often included in anthologies. You can lookup the cross-references for the Bible text to expand them. 

The Catholic Topical Index section provides a larger list of scriptures and patristic sources:

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BISHOP (Episcopate)

Sacred Scripture
NT Ac 20:28, Tt 1:5–11, Jn 20:21–23, Mt 28:16–20, 1 Ti 5:19–22, 2 Ti 1:6–7, Ac 6:6, 14:23, 1 Ti 4:14, Jas 5:14, Mt 18:18, 1 Co 11:34–12:31, 1 Co 14, 2 Ti 4:2–5, Tt 2:1, 15, Re 2–3, Ac 2:42, 1 Pe 5:1–3, Mt 10:40, Mk 16:15, 20, Lk 10:16, 22:19, Ac 1:8, 2:46, 8:5, 14, 38, 15:22, 28, 19:6, 20:7, 17, Ro 1:5, 1 Co 4:1, 21, 2 Co 5:18, 20, 1 Ti 3:1–13, Mk 3:14–19, Lk 6:12–16, 22:26–27, Jn 21:15–17, Php 1:1, 1 Pe 2:25, Mt 16:18–19, Mk 1:25–26, 6:7, 13, 10:45, 16:17, Lk 24:47, Jn 10:36, 17:21–23, Ac 2:4, Ro 12:4, 1 Co 9:1, 11:26, 15:7–8, Ga 1:1, Eph 2:20, 2 Ti 1:13–14, Heb 5:1–10, 7:24, 9:11–28, Re 21:14

Church Teaching
Catechism CCC 1555–1570, 861–862, 879–887, 893–896, 1576–1577, 77, 816, 857, 873, 877, 919, 927, 1120–1121, 1142, 1184, 1297, 1299, 1312–1313, 1369, 1462, 1483, 1538, 1549, 1572, 1594, 1673; Glossary “Bishop”, “Episcopal/Episcopate”; Index “Bishop”
Denzinger DS 1767–1770, 3061, 2592–2597, 3050–3052, 1777, 215–216, 793–794, 944*, 1265, 1774, 2609*, 3011, 3804, 308, 785, 831, 860, 1069, 1178*, 1260, 1317–1319, 1326, 1463*, 1612, 1617, 1630, 1710, 1719, 802, 1609, SCD 52d–e
Papal Encyclicals Fidei donum 42, Redemptoris Missio 69
Canons of the Ecumenical Councils Nic. I, Canon 4
Vatican II LG 19–23, 26–29, CD 2–4, AG 5–6, CD 33–37, PO 2, SC 41, LG 10, OT 20, DV 7–8, AG 38, SC 35, LG 8, 41, UR 3, CD 9, 15, AA 2, 16, AG 16, 18, 40, PO 8, 10, 15

Canon Law
Code of Canon Law CIC 336, 961, §1–§2, 207, §2, CIC 330, 337, §1, CIC 591, 605, 844, 882, 883, 2°, 884, §2, 962, §1, CIC 967–969, 972, 1172
Code of Canons of the Eastern Churches CCEO 722, §3–§4, CCEO 744, 747

Ecclesiastical Writers
Apostolic Fathers 1Cl 42, 44, ISmyr 8.1–2, IEph 3.2, ISmyr 9.1, IMag 6.1, ITr 3.1, Poly 5.2
Apostolic Traditions APTR 8
Apostolic Constitutions Const. Ap. 8.47.35, Const. Ap. 8.27, 3.20
St. Justin Martyr 1 Apol. 65, 67
St. Irenaeus Adv. Haer. 3.3.1, 3
Tertullian De praescriptionibus adversus haereticos 32
St. Cyprian De laps. 29, Cyprian, Ep. (O) 73.9, Cyprian, Ep. (O) 75.7
St. Gregory Nazianzen Orat. 2.22
St. Athanasius Ath., Ep. Afr. 2
St. Ambrose De paenit. 1.2.7
St. Jerome Ep. 146.1, Lucif. 9
St. John Chrysostom Hom. Act. 18
St. Leo the Great Ep. 108.2
St. Gregory the Great Regist. 1.25, 11.64
St. Thomas Aquinas SCG 4.60, STh., III q.72 a.11, Supplementum q.38 a.2

See also: Collegiality; Apostolic Succession; Hierarchy of the Church; Holy Orders, Sacrament Of

Andrew Jones et al., eds., Catholic Topical Index (Bellingham, WA: Verbum, 2013).

The Ancient literature section is not topic oriented but if you take a significant Bible reference, it can also give you relevant source with some overlap with the Catholic topical index.

Those three sections of the Passage guide - cross-references, Catholic Topical Index, and Ancient Literature should be starting points for any research that includes history of ...