How to ask a girl out... I'm so terrified?

I've been friends with a girl I know though work for a few months now. We've gone out to the movies a few times and had dinner together, not on a date but just as friends. However I have developed romantic feelings for her and I'd like to ask her if she'd be my girlfriend, however there is a big problem. When it comes to women, I'm more or less clueless. I suffer from social anxiety and as a result I've never really had a girlfriend before at 26. I'm really, really shy, and am pretty awful at expressing how I really feel. I'm not good at reading signs, I'm not good at sending signs, and even if I were, I wouldn't really know how to follow up on such signs. Not only that, I have a deep seeded fear of rejection.

I don't know what to do, sometimes I wonder if I should bother asking her out at all, knowing my luck she won't feel the same way I do but I do like her. Anybody have any ideas? Particularly as to how to ask her out?
How to ask a girl out... I'm so terrified?
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