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.
Your statement is wrong, it's not about the anonymity of Bitcoin. It's about the decentralization of Bitcoin
a bank would not very much fit with decentralization too IMO.
some european banks were working with europan exchanges but not directly though and they closed their account afterwards, hard to see a bank dealing with bitcoin