It's just too hard to explain to people. I tell them how great it is and that I'm mining for Bitcoins and buy things with them. Then I need to go through this whole process of trying to make them understand. What a pain in the ass. There is no way banks would ever go through that cost. There is no upside for them to do it. Give me an argument I can use to tell people i'm not crazy, one thing that Bitcoin can do/buy that a Visa card can't. No fair using Silk Road my grandmother doesn't shop there anyway. Don't use hide from the IRS either she would think that's wrong.
Established banks wouldn't want it to succeed, let alone support it. Luckily for us, we don't need banks, we need software developers.
Consider how Bitcoin would grow if it was integrated to eBay. It would be better for eBay too, because they would be the escrow service, and wouldn't have to worry about external entities, fees and chargebacks. It would also be better for sellers and buyers for similar reasons. Plus, you would trust their wallet service so it would be instant and "easy to use".
Anyway, why do you yourself think it's a good idea? I think you should begin with that. Yet, again like Linux, it can be hard to explain. I use Linux because I want the whole control of my system, I want it to do my bidding to the extend it can. I can't explain this to an ordinary Windows user, you have to experience the need first. You need to know what you can do with a computer and it must be worth your time. Usually it isn't, because you've already invested time on learning a different system which in the meantime taught you what you want to do with it.
Pretty similar to our dominant monetary system, don't you think?
Society gets stuck like this. IMO, online bank accounts are much more complicated than Bitcoin. And they don't have a standardized interface. Yet, people use them because they have to. Credit cards aren't inherently easy either. People need to see "someone else use it" and imitate, that's how Bitcoin will go mainstream. We need a payment method that reptilian brains can imitate. I think foolproof standardized smartphone POS interfaces would suffice.
All in all, I'd try the "when there is frictionless value transfer globally, possibilities are endless" approach.