Long distance relations CAN work.
People that say they NEVER work haven't had it work for THEM. Doesn't mean it can't work for someone else.
And as I say that, I'm currently in a long distance relationship that's been going on for over two years.
At first it was just Skype/voice over internet for the first two years. We really became internet pen pals I guess you could say, but with a lot more emotional attachment and feelings towards each other.
Just this past November, we decided to meet. I live in Chicago and she lives in Montreal, Quebec Canada. I went there, spent a week with her for her birthday, and it was one of the greatest times of my life.
After that week, it really solidifed our relationship to something more concrete and real, and since November I've been back 3 times.
Let me point something out also, you are NOT dating someone if you haven't met them yet. I don't care if you spend 10 years talking to someone. Until you MEET, you haven't experienced everything that person is about. Meeting is what makes or breaks the deal. Until you've done that, it's not official.
If you've already put time into this, don't worry about meeting her. You don't have to "ask her out"....I think by the time you both get together, it'll either click between you two or it won't, but you don't need to ask for it. It'll just happen if it does.
Good luck to you.