He is not off limits just because he is your dance instructor. If you want to broach the subject with him, then go ahead. I have seen several relationships work out. Two were female teachers with male pros and one was a male student with his female pro. Be warned, you may see less of him than you do now. Since he owns his studio and is busy and successful, he will be working evenings and weekends.
You might be one of his favourite students, easy and pleasant to teach, so he laughs and jokes around with you and enjoys the lesson. That doesn't mean he wants the relationship to go anywhere. Why don't you try booking the last hour of the day and then suggest you go for coffee or a drink afterward. If he seems keen, then you might be on to something.