i do not think so that still there is any kind of bank our any other bank yet consider bitcoin as legal currency. but hope that a time will come when banks will accept bitcoins.
The concept in the bitcoin are not relying on the another party, the true concepts of bitcoin are making your own bank in your hand and all of the control in you. talking about the another kind of bitcoin bank is already out from the concepts of bitcoin but in bitcoin just know about the wallet and the wallet providers.