Ah. Social proof makes women 100x more receptive to your advances. She may, at first, be a little guarded cause you may be overqualifying yourself. If you're getting positive signals from all the girls in the room she might think you're a player. Catch her in the hallways and ask her when she's at her lockey. If you ask her and she's seems a bit uneasy about it, just persist a little bit more. She may think "why is this guy who has all these girls interested in him asking me to the prom?" Tell her that you want to take her cause she's a cool girl and you'd love to accompany her to prom.
You'll do fine. Please, PLEASE, don't avoid asking her to avoid rejection. It's not as big of a deal as you think.