I guess some third part also can work as intermediate to accept bitcoins and deposits corresponding amount into their accounts. This way we can make banks accept bitcoins virtually.If you consider online payment processors as online banking, then many processors accepts bitcoin for depositing and withdrawing funds.

There is no bank for this. I guess this was the whole idea of bitcoin, to be stored online not in a bank

I do not think there is but there will be. Here in our country, government starts to support bitcoin and some stores already accepting bitcoin as a payment method. And the most important of all is the fact that the Central Bank of the Philippines is acknowledging bitcoin, I think this would be great in my country because they are open-minded about bitcoin. And maybe months or a year later they will be legalizing Bitcoin as a payment method. This would be great for the investors, especially to the Filipinos. government is doing such a good job on supporting bitcoin. But there is a question in my mind, will they allow it? Because banks see bitcoin as a big threat to them.

I suggest you to create a wallet in spectrocoin and you can order a debit from the site. In my opinion, it's better to use an exchanger that converts bitcoin into fiat money vice versa. Thus, bank wouldn't need to change their systems and the service would be better.

I Guess that there is isn't any Bank accepting directly bitcoin yet. I heard Barclays is very friendly towards bitcoin. but still they do not accept it. However, I think it is a matter of time until we see a Bank start to accept bitcoin

Yes I am sure there is , but honestly, don't know which myself. Would be interesting to have a whole list of banks.

As far as I know, since the Japanese government accepted Bitcoin, it means the banks of this country also accepted Bitcoin since that time. However, recently, a bank from different country have accepted cryptocurrency too, not only Bitcoin. You can read this article to know more details: https://www.coindesk.com/liechtenstein-bank-opens-up-cryptocurrency-investment-for-clients/

I think there are some banks that accept bitcoin bitcoin has value because of the very high and very high popularity bitcoin.

a banker who is a friend told me,banks are jittery about em.don't know how true that is

What do you mean directly?if directly i think no because many people don't know about it. So we need to deposit it online through my local wallet. But i read it in some articles about bank accept bitcoin.  In nigeria news i read it that bitcoin there are so important they some banks accept it.