I don't see how will a Bitcoin bank work. I have definitely seen people giving small amount of loans on Bitcointalk itself. But here we are talking about comparatively large organization(centralized) to give loans at big level. Why it won't work is because supply is way too limited along with that the availability of bitcoin in market isn't much as most of the people are merely hoarding it. Bitcoin is highly volatile. These all factors makes lending inefficient.
i think people are already fedup with traditional banks, therefore they may not be too much interested in bitcoin bank, i think using wallet is the best way to use your bitcoins.