fusangite said:
Basically, I am a pretty socially perceptive person in most situations -- until it pertains directly to me. Then I turn into a complete moron.
That’s most people, I think.

it’s often way too obvious when someone is flirting with someone else, but when it happens to me I’m never sure.
I have to agree with people that say tread cautiously, and with those who say you need to talk with her outside of gaming.
Tread cautiously, if it’s important to you as the DM to have her as a player in your group, or even as a friend. If you try to put the moves on her and fail, that will lead to all sorts of awkward situations, and ultimately will probably end in her uncomfortably leaving the group. Of course, it may not go that badly, she may just shrug it off and say “eh, it’s happened before.”
And yes, you definitely need to talk to her outside of gaming. If all the time you’ve spent with her so far was playing an adult version of “make-believe,” how can you possibly know her as a real person?

When you do get a moment to chat alone (or with at most one or two other people around), don’t talk to her about gaming, and don’t ask her out until you’re comfortable that it’s a good idea. Talk about a movie you just saw, a book you just read, or a song you just heard, or ask her if she’s got one of those to talk about. Small talk, while generally banal, is a good way to feel out where someone else is coming from. If you can’t get onto her wavelength early on, you’re probably not going to do it later either. Keep it casual at first, and go wherever you feel comfortable when you are ready. If she doesn't pick up on your signals, you can always just play it cool and just keep her around as a friend/fellow gamer.