Thanks, guys, for the helpful answers.
I just reinitiated contact with her yesterday on Facebook. I asked her to evaluate the nerdiness of my current profile pic on FB (kind of an opener). She gave me a "two-word" answer, but I digged in deeper on the topic (I told her the background story, that I was competing with my friend to see who will have the nerdiest profile pic on FB, and wondered if she could give any suggestions for being more nerdy on picture) and let's see what she says next. She's kind of a nerd (she reads tons of books) and an Honors student so I mentioned that "you are qualified to answer this..." in the first message.
I will tactfully invite her to a potluck party my friends and I are hosting this weekend. The reason I will give her is "we would like to have each person bring a new and unique face to the party so that we can be the most diverse and unique group" (most of my friends are international students and cook very well). "And I think that you'll be a refreshing element that'll stir up the group, if you behave

" Do you guys think that this will be a sound reason and a friendly "challenge" for her to join my potluck party? Any better suggestions?