It is rude for a man to turn down a dance invitation from a lady, even if she is a stranger. It's just the etiquette. If you don't want that to happen, do not visit such public places, because most likely there will be a lot of stangers.
If she was in control, he wouldn't be dancing with other women. Next time, you go ask a gent to dance with you. No harm in that, right? Maybe then he will feel the way you did. Or he may beat you when you get home???