I highly doubt there would be a bank for bitcoins because the whole point of btc is for it to be anonymous and that bank will totally destroy that ideal.
Now more than 400 European Banks Allow Direct Purchase of Bitcoin European banks have now joined the main retail list to receive Bitcoin directly. Currently, Bitcoin becomes easier in its transactions if you have a bank account in most European countries. All you need is to be a member of one of hundreds of banks, and you can buy not just Bitcoin, but many other cryptographic currencies too quickly, and easily. It includes over 400 banks in ten countries (Germany, Austria, Switzerland, England, Netherlands, Belgium, France, Italy, Spain, Poland). This will allow 99% of all banks in Germany to accept Bitcoin purchases through 247Exchange. Slovenian and Hungarian Banks have not issued an addendum as this Agreement.
yes there are a lot of banks who accept bitcoin and one of the indian bank also accept bitcoin in my country there are alot of private bank who accept bitcoin .