Banks can't work with bitcoin, search "fractional reserve". Banks may offer some Bitcoin services in future but it won't replace fiat services nor it will be possible to seamlessly juggle/ exchange between bitcoin and fiat.
In my country (Ukraine), in a bank digital wallet, it has long been possible to transfer Bitcoin and use it for shopping. True, from this wallet it can no longer be withdrawn. In fact, after transferring to the wallet, the bitcoin itself is withdrawn from the wallet by the bank, and we have the opportunity to make various transactions for the sum of the bitcoin value in online mode. That is, the purse continues to indicate the amount in Bitcoin and its equivalent in local money.