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.

There are no banks who accept bitcoin, but with the majority of banks you can withdraw money to an exchange and buy bitcoin.
I use kraken and when i want to buy bitcoins i just iniatiate a SEPA transfer and voila i can buy bitcoin.

I can't think of any bank accepting bitcon, Bitcon is their no1. competitor. Some banks even block your account if you are affilaited with bitcoin..
So be carefull. I for one never use bitcon in the message field when i make a transfer or buy some bitcoin related gear.

Issuing Banks are supporting new Program Managers that are entering the Bitcoin space, see Shift Payments program issued by MCB out of New York.  One line of thought is comparable consumer products; landline telephony.  There was a dramatic shift of consumers from landlines to mobile 15 years ago.  Eventually a new demographic emerged that skipped land lines completely.  In the same thought line with Bitcoin globally supported, and smart phones continuing to bridge financial service gaps, "self banking" is a reality to end consumers (non innovators).  Brick and mortar financial institutions are on the decline...  Small banks will use this opportunity to grab marketshare by playing within CFPB and OCC recommendations of OFAC and CIP.  Larger bank entities will not want to lose their market share.

Just look at the job opportunities on Ladder for example, Senior Vice President of Cryptocurrency Development.  The banks are posturing for acceptance.  Fidelity, Chase, etc... nobody is going to go in front of their Board of Directors to say we missed the boat.

This is bigger than customer deposits at your nearest Wells Fargo.

Time will tell.


EDIT:  Im in the US and grammar.

I don't know about the real banks, but i know that some electronic banks online accept Bitcoin already for deposit and withdraw, like Payza and Neteller and so on. Of course you can use this electronic wallets to charge your real account in your bank

I've seen some A-ads advertisement advertising a bank that accept Bitcoin. However I actually did not click on these advertisement as those look scammy. Well, why would bank accept Bitcoin a very unstable currency? Just two days back, the price went from 400 to 475 and drop back to 400 all within 24 hours. With this very unstable prices, which businesses will lend Bitcoin from banks? No businesses unless it is Bitcoin related. Thus, with no businesses lending Bitcoin from banks, how do they pay people interest?

No very certain that does not exists. No money to me made for the banks with Bitcoin, they hate it

In France, Paymium is officially recognized (and you can use it in many European countries).
You can use services that will be "like a bank". Xapo for example will keep your bitcoins and give you a debit card to withdraw and pay in FIAT, that can be considered as a very simple banking service.
You can also "lock" your stash into USD on a service like coinapult, it can be useful for small e-commerce if you don't want to deal with volatility and also don't want to deal with -for example- BitPay.

It is too violatile for any banks to hold the risk. Violatility will cause customers to make frequent transactions that adds to overhead costs of running the business.

I'd give it at least 2 more years before they successfully incorporate bitcoin into their systems. I mean they'd have to pretty much redo most of their legislation to comply with national laws and whatnot. Being a bank you get the perk of integrating new stuff really slowly.

So to answer you question, no currently no bank accepts bitcoins. There are many banks however that show interest to bitcoins.