i don't think that there will be a special wallet that can be used for bitcoin and the bank, its better to have each of wallet for bitcoin and bank. i think if bank is using the blockchain technology, then bitcoin will be include in the transaction and can be act like fiat as new type of money.
I am new and curious also, as per i know the core purpose of bitcoin is to decentralized the wealth,But if bank stating using it banks will hold and significant number of bitcoin and then they can control the price and make it centralized cause they will hold our private keys.Am i wrong with my point still confused.. 