I don't know if saying you talked to her "on a dare" is a good idea... that can get taken in negative ways... she also might not appreciate being the object of a bet. But it depends on the person. For an out of the blue introduction you may want to avoid that since you don't want to take a chance on insulting her.
Since you're in the same class you can offer to study together in a public place or if she asks a question in class approach her like you're following up. It would be better if you actually were, but we all do what we can. Meeting people from across a room is difficult.
Ed Womack
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