Full speed ahead, tell her how you feel. It can only end in two ways:
Your dream becomes a premonition and you live happily ever after.
She tells you she doesn’t feel the same way and it ends there, awkwardly or not.
Speaking from experience. I had a crush on this one girl and I just couldn’t get her out of my mind. I decided to do something about it and asked her out. She said no and that was the end of it.
Don’t be afraid to be awkward.
Edit: If this truly is an impossible situation (you or the instructor are already in committed relationships) then I agree with everyone else telling you to find another instructor.
OR
Still do what I said but try to reconcile your feelings for her, with her. Also speaking from experience here. If she is a dance instructor, she is probably no stranger to having her pupils develop feelings for her.