I dont see any bank directly working with bitcoin exchange, it is exchanges who are buying and selling the bitcoins through their banks or through their own way. no bank work with bitcoin as they are against bitcoin.
Bitcoin exchanges needn't buy or sell Bitcoins themselves at all. Their customers provide the liquidity, so an exchange only needs to be able to receive deposits and pay out withdrawals.
To that end they certainly work directly with banks. For example, Kraken works together with Fidor.