No there is no bank or financilal institute which accepts bitcoin as a payment as per my knowledge.

No I don't think that any bank in the world accepts bitcoins but all I know is that they accept payment from the bitcoin exchanges, so what I do is that I sell my coins on exchange and then transfer those funds to my bank, so indirectly my bank is accepting the bitcoins.

Same process on my local exchange too which they are being used on their service which i do make make some conversions of my bitcoin to local fiat and directly send it to my bank account by the use of local exchange which is really great and same as you said it is an indirect way.For now i havent see any banks that do make use on bitcoin knowing that they wont really tend to tied up with it.

In my own opinion, I do not think that the concept of accepting bitcoins in bank or transfering your coins to the bank is a good idea because your coins are already growing even by just holding it so there is no sense in placing it to the bank, unless it will be mandatory for government because they will place tax on it obviously.

I think all these banks deal with bitcoin.
USA
itBit Trust Company, May 2015  <---- First US Financial Institution to Accept Bitcoin
Wells Fargo Bank, N.A. takes deposits for Ripple, August 24, 2014
Bank of America takes deposits for Ripple, August 24, 2014
Capital One takes deposits for Ripple, August 24, 2014
Capital One 360 takes deposits for Ripple, August 24, 2014
USAA takes deposits for Ripple, August 24, 2014
TD Bank takes deposits for Ripple, August 24, 2014
US Bank takes deposits for Ripple, August 24, 2014
PNC takes deposits for Ripple, August 24, 2014
Chase takes deposits for Ripple, August 24, 2014
Bank of America, BAC, initiated analysis coverage of Bitcoin December 5, 2013

Canada

Bank of Montreal, BMO, of Canada, open to dealing in Bitcoin transactions subject to more regulation. April 1, 2014


EU
Handelsbanken takes deposits for Safello, and so do a bunch of other EU banks, December 15, 2014.
Fidor Bank AG, of Germany, integrates the Ripple Protocol. May 6, 2014





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None of them are accepting bitcoins or bitcoin deposits.
They are dealing with exchanges like coinbase but only in fiat terms.
There isn't a single bank which accepts coins directly and stores them as btc deposits.
The only few projects involve a middle man which will exchanges your coins for fiat and it will deposit the usd to your account but that's just a simplified exchange. Even so called bitcoin cards work on the same principle.

PS.
I've deleted your last phrase..that's pure advertesing spam.

Bank Seed Cannabis Receives Bitcoin,
The company's mission has always brought an eclectic mix of cannabis genetics to farmers around the world. Internet and Bitcoin have enabled companies to reach a wider audience.

"Bitcoin allows our customers to pay with digital currencies and is not tied to one country," explains Alex. "It provides a safe and secure alternative payment method that has proven to be very popular, especially by those who care about privacy.Once set, Bitcoin is very easy to use and has become a preferred payment option for many of our customers."
http://www.fulus.com/forum/threads/bank-seed-canabis-menerima-bitcoin.3067/

I don't think so, the thing is the banks only accept money that is in a form of cash. It's like they cannot store something that has a physical form to give it value. Unless, the bank adjust to accept, or they make a physical form of bitcoin.

There will be no bank that will accept BTC deposit because that will go against the basic principle of BTC that is decentralization. But nothing is impossible may be banks may embrace blockchain.