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.
Well, I think there are still no bank that accept bitcoin as a deposit of their costumer.Furthermore,bitcoin doesnt have exact value in every time the value of bitcoin can change so that if theres a bank can accept bitcoin I think they cant handle it. I hope in the near future some bank would accept bitcoin as deposit of their costumer.