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.
Everything is possible, and I believe a time will come when the bank will be the biggest and safest exchange because Bitcoin is still growing. We can see how many countries are accepting Bitcoin and also developing a Bitcoin reserve.
If the governments are now friendly with Bitcoin, then it is possible that one day the bank will have something to do with Bitcoin, and it will be a great advantage to the bank because the bank will be more reliable than online exchanges. There won't be cases of theft and scams like what is found on online exchanges. I'm very sure that in a short time, we can have this.