I have no direct knowledge about bank acceptance but my colleague who is now earning from
Bitcoin had her transactions made thru bank so I guess it is accepted. And as far as I know there is no policy prohibiting the same.
Most of the countries on the world did not ban Bitcoin, only some countries and one large country (China) banned Bitcoin because the government of these countries feel Bitcoin as a threat for the future of their countries.
Recently, few banks accepted Bitcoin for investment and loan from Visa/MasterCard.
Example Liechtenstein bank opens up cryptocurrency investment for clients in the last month, it proved Bitcoin can get accept from the bank in the future.