As long as this thread doesn't get all MadBaggins
-y, I'd recommend that you start small before asking her out. Simple, friendly conversations to start out and then eventually ask if she wants to get some coffee after class (give it at least two weeks of regular contact). Take it slow, and don't give her the impression that you're in love with her or anything.
Don't do that thing with the story, that's kind of creepy. Just write a good story man, make it light and funny. Don't make it personal, don't put her name, or pieces of conversations with her in it. just write.