I think that the "bitcoin bank" name is misleading. In my head (and others' too) Bitcoin bank would be a "bank" where you "deposit" Bitcoin and get interest. Of course, such thing could not be great and it's not what you ask for.

So a better name could be "Bitcoin friendly bank" although there are already a couple of banks or banking services that are not that "cold" towards Bitcoin, allowing withdraw from exchanges and also offering services to buy Bitcoin for you.

I guess that you know all this. What I want to say is that we already have a few "friends" and the banks overall seem to get more friendly towards Bitcoin with every new day passing. So a bank offering full services, from exchange (or work with an exchange) to cards and such is just a not-so-far step. Incorporating Bitcoin capabilities into their ATMs is also a not so difficult next step. We are close to that, your 10 years number may be already big.

The question about the demand is, however, a very good one. Banks usually operate with high fees. So although more convenient, buying/selling Bitcoin though a bank will be more expensive (in the same way converting EUR/USD/local currency is much cheaper at an exchange office than at the bank). There will be demand for it, but I don't think it will be that big. Of course, it will add legitimacy, which will translate into increasing demand.