There are no banks who accept bitcoin, but with the majority of banks you can withdraw money to an exchange and buy bitcoin.
I use kraken and when i want to buy bitcoins i just iniatiate a SEPA transfer and voila i can buy bitcoin.
I agree that there are still no banks who accept bitcoin. In addition to that, I guess that if there is a bank who totally accepts the bitcoin I think they cant handle it well because bitcoin doesnt have any exact value. However, I think in the near future there will be a bank who allows bitcoin as deposit of their client.
I doubt that banks will take bitcoin. They do not need such a strong competitor. I think that they will convince all citizens that it is impossible to trust cryptocurrency, and all the savings need to be kept in a bank