I don't think there is any Bank yet which accepts Bitcoins as a currency.
Furthermore i think.. noone would deposit bitcoins there.

I don't have any knowledge too that there's a bank that is using bitcoin for their service like bank deposit or even loans. I also doubt that there would be people that are going to allow the banks to store their bitcoins. There are a lot of ways to store our bitcoins because a lot of trusted wallets are there for us to be our very own bank.