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 bitcoin bank will be a online bank with all the facilities of the real world bank as bitcoin bank will not need any physical infrastructure and other things. Bitcoin can become a global currency one day and then we will need this bitcoin banks to keep your money and also get interest from it.
As well there are many new investment sites like Bit connect are launching which gives a good amount of interest to the investors it is also a step to create a bitcoin bank where people can keep their money safe and also gain a monthly interest.