First, your self-esteem seems to be OK. Be thankful for that.
Second, and I'd like to raise this point here, there is a difference between being able to have a good, fun conversation with someone and being able to ask them out, at least from my perspective. It requires you to look at yourself as a potential partner rather than just someone who can go up and talk to people. This switch in modes of thought is hard for some people, especially if they are shy or late bloomers socially.
So, I want to emphasize the point made above that exposure is really the only way to inure yourself from that sort of thing, and not necessarily just social exposure either. Even if you can go up and talk to someone, it doesn't necessarily mean you're out of the woods yet.
Maybe I'm generalizing from my own problems, but it doesn't seem like you have trouble talking to women per se, just, you know, _talking_ to women, if you get my meaning. So that's what you've got to do. Painful, I know, but there is no growth without pain.
Some of the suggestions above could be useful in this respect... any others?