Thanks for all the suggestions. Still haven't made much headway.
I did a restore with 9.2.1 then updated my phone from the backup. I'm starting to think something is corrupted there and that's the problem.
When I open iBooks I get the little rotating circle icon next the the wifi indicator at the top left of the screen. It'll stay open for a little while -- from 1 to 5 or so seconds -- then the app closes. If I double click the home button the app is still running. I can open it but the same thing happens and it usually closes faster than if I'd just opened it or if I opened it with airplane mode on then turned airplane mode off.
I've noticed I have some .pdf files in Settings in iTunes that I can't sync.
If I check the boxes and click apply or sync nothing happens. I added another .pdf file this evening and it synced just fine. I can't figure out any way to delete the files from that list.
Could there be a problem with iBooks crashing because it's trying to sync bookmarks or some other data from those files and failing?