Bitcoin is a decentralized currrency.I think its higly impossible for any person or a group of people to form a bank for bitcoin.Already,there are exchanges for buying and selling bitcoins,wallets for storing bitcoins and other than this,i don't know what difference a bitcoin bank could make.

So,with our private keys secured,we ourselves act as bank by holding bitcoins in our wallet.So,bitcoin bank would not come in to reality.