I highly doubt there would be a bank for bitcoins because the whole point of btc is for it to be anonymous and that bank will totally destroy that ideal.
Indeed, you are right! All banks are centralized or regulated industry while bitcoin is not centralized. although bitcoin for some other banks butcoin for them is a threat to their business. But the reality is not, instead bitcoin is very open type of source to any business.
I don't think there is any bank at a moment that is accepting bitcoins and even I don't see it happening even in future as bitcoin is a competitor to the banks so I don't think that banks will ever stand in support of bitcoins or will start accepting it.