I think that is impossible because we still need the bank as a medium to withdraw funds from bitcoin wallet against the legal currency in our own country. However, if bitcoin is legalized all over the world, the bank may still exist but bitcoin can enter as a recognized currency in the bank and can be used for direct transactions.
Why do you need bank as a medium? You can convert Bitcoin to fiat cash online, using any of the exchanges. Or you can use pre-paid debit cards and load them with BTC. Once this step is complete, you can either use the funds for shopping, or you can withdraw the money using any of the ATMs. Banks are not needed at any point of time.