No. i dont think any bank accepts bitcoin because bitcoin is not controlled by the government and all the banks are being controlled`so i think that those 2 won't ever combine because bitcoin is a unstable coin aswell.
No few banks is accepting bitcoins, as you said it is controlled by governments and they have not permitted the use of bitcoin, once they permit can use the bitcoin.
as far as I know each country is different, so banks are also different determination, there is a permissibility and not. it's all how the government takes care of it.