Have you talked to your girlfriend about this?

While your situation isn't common, it's also not rare-- I've talked to more than a few couples in the same position as the two of you. Of course, it's not a bad situation to be in-- you've had a relationship for six years, and you can be confident it's not based on sex.

But maybe you want to take it farther now. After so much time together, you are probably ready. But you have to talk about it first.

If you haven't already brought up the subject with her, it can be hard at first, but the next time you get an opportunity to talk privately, say something like, "Well, I've been wondering, we've been going out a long time-- I'd like to do a little bit more in our relationship sexually."

Don't be demanding, but be direct. At worst, if she's not interested, then you've been going out long enough she should still be polite about it. But chances are, she might be feeling the same; it's just she's shy as well.

Of course, whatever you do, always practice safe sex ;)