One day banks will accept Bitcoin as medium of exchange and accept deposits from bitcoiners. As soon as the world powers accept it as medium of exchange.
No doubt it will happen but be sure to bend according to the policy set by bank to any Bitcoiners that would be depositing Bitcoin into bank, a lot of strict regulations will be passed to complete KYC verification, minimum and maximum amount and more which will actually control the customers hindering their full potential.
Also, the withdrawal and deposit fee banks can be charging will be too high.