Personal books are not currently available on mobile.
Make sure to cast your votes on the uservoice suggestion for this!
https://logosmobile.uservoice.com/forums/190765-logos-mobile-apps/suggestions/3625331-pbb-sync-to-mobile
The last update they said on this suggestion was:
PBB Sync for Desktop is in progress, the feasibility of PBB Sync to mobile will be examined after that is completed
Well now, with Logos 6, PBB Sync for desktop is complete, so I'm hoping that they will soon change the status of this feature from "under review" to "in progress"