Adventurers should be sent across the city and across the depths of the Underdark to retrieve overdue library books from patrons who took books out but did not return them on time. As a reward, players should get a small portion of the late fee. Since these are late fees for library books, the bounty might be something in the realm of 3-5 gold per incident.
You're a madman, but I'm totally fine with risking life and limb for 3 free gold
Could be a way to get people out of Sanctuary and its surrounds if some of these requests had instructions on how to get somewhere really off the beaten track as well.
There already is a library get me books quest that sends you hither, thither, and yon. I think any new bounty system should be added to a location that doesn't already have one. (Lower, Mur, Sorrowfeast, etc.)
Could accumulate favour points to be cashed in for monk scrolls, scrapper schematics, or wizard scrolls.
Or/and perhaps with a good enough track record, access to book bounties of much more sensitive nature (Ambient quest that doesn't happen often, randomised, group oriented, more impressive rewards..)