In order for a bank to start accepting bitcoin, there has to be an agreement reached. Perhaps a third party bitcoin provider but this would surely have additional costs attached to it. And right now, there is really no need for bitcoin to be accepted in banks because bitcoin can serve that purpose already. I also doubt if bank tellers know anything much about bitcoin as they sometimes are not even familiar with their own services.
banks should not do bitcoin transactions, because with the service they have been doing so far classified as a lot of transactions, because bitcoin transactions require handling very different from like a general bank. may even need to learn more carefully and transactions that occur are also very high risk.
if possible, it may be possible but better stand alone and not join the tub in general.
