Crush and Prom Help!?

So before I give details, please don't think I'm crazy, but I have a crush on one of my teachers at school. But her and I are pretty close for a student-teacher relationship. I talk to her about random stuff around once a week, and if I don't have conversation with her I at least make a point to say hi to her at some point. I know a lot about her and she knows a good amount about me. However, she is of course a teacher and she's also engaged to be married next summer. I am a Junior, and our prom at my school is in the fall, this Tuesday. As crazy as it sounds, I asked her if she would go with me, but she said she couldn't, but she said she might be there as a chaperone or just to see everyone dressed up if she was free. It turns out she's chaperoning, which means she'll be there all night. In the meantime before knowing that, I didn't ask anyone else to go with me, so I'm one of the small amount of people without a date. I'm not the only one without a date and there are girls without a date, but the girls I would have asked already have dates. I'm fine with going alone, but I want to spend some time at the prom with this teacher. I'm definitely going to talk to her and I'm probably going to take a picture with her, but I kind of wanted to ask her to dance. I'm really doubtful that this is a good idea though. Should I ask her? If not, what else can I do to have fun alone at prom? Other things? Thanks for your help!