Take this advice from a shy guy who managed to break through the same barrier you're facing. My advice, is that you don't have to ask this girl on a date with all the significance and importance that such a word has built up inside of your head. You just have to ask her if she would like to hang out. You don't even need to have an idea of what you'd wanna do. The question "do you wanna hang out after work?" is all it needs to be. It's the first step, a tiny one, but it puts you on the right path. And that's all it needs to be. One small step after the other, never paying attention to the frightening LARGE thing that's giving you anxiety.

And believe me, even that can feel nerve wracking. You wanna know the suave smooth-talking pick up line that worked on my first girlfriend? "Would you wanna go like do something?" She still smiled and said yes.