First of all, you all that have answered so far gave some really good insight on Bitcoin, but that does not answer the  question (If I am understanding the question correctly).  I am sure that someone else will still have this same question. In that case, I will give my best attempt to answer the question that i asked.

I think that the people that have so far answered the question didn’t realize at the time of posting their answers didn’t realize that banks are actually allergic to Bitcoin. What do I mean by that? Well… Before you do any kind of serious trading or transactions with Bitcoin, you must first have some things in place. For instance, you must have an anti money laundering agreement in place. People think that profits from Bitcoin is tax free. The IRS doesn’t see it that way. Bitcoin profits are taxed as capital gains. So if you’re going to do any kind of significant volume using a bank as a middle man, you have to have things in order, or else, they will shut your account down and you may even see a negative balance. Bank of America is notorious for shutting down accounts!

To get a good idea about which banks are most Bitcoin friendly, I suggest that you visit Bitcoin News, Blockchain News, Prices, Charts & Analysis - CoinDesk and inquire within the community.

I hope this helps! Just keep in mind it’s going to be more so about that anti money laundering paperwork than it really is about the bank itself.