There does not seem to be any bank accepting bitcoin, at least I do not know about it, bitcoin is an emerging thing after all, and banks do not allow customers to frequently roll out and switch to bitcoin every day. . .
As we realize that bitcoins was presented in year 2009 so it's no excessively old that is the reason banks are not tolerating bitcoins but rather don't be stressed in light of the fact that soon they will change their strategies yet it will require some investment and after that the banks will likewise acknowledge bitcoins and will begins saving money with bitcoins and will acquire more cash in bitcoins.
Yes currently they are not accepting bitcoin because of their government policies, but in future specially when their government will turn bitcoin as legal currency then we can expect that banks will also start accepting bitcoin, because they can also get good profit from bitcoin in form of transaction fee.