I taught ballroom dancing for a little over ten years. Here's my take.
The unwritten rule in the industry is that the instructor does not date the students. I've seen this rule broken on several occasions and it never ended well.
What you're seeing when you come in for a lesson or go to a studio party is the very best your instructor has to offer. You do not see all the crap that happens outside the studio, nor are you seeing what happens behind the closed door of the teacher's lounge. Believe me, the two are vastly different.
Your instructor is in a position of power. He's an expert at emotional manipulation. We used to spend hours practicing flirting and manipulation in front of other instructors, and with other instructors heckling us. The theory being that if you could say it convincingly under the worst conditions we could provide, it'll be a cinch on the floor. We were right. I, when I was in the business, could say absolutely anything and be believed.
Your average dance instructor has the ethics of a chainsaw. It isn't that he doesn't care about you; he does. Just not as much as he loves that money.
So do not start dating this man. Or woman. Just tell him 'Thanks, but no thanks.'
If you ignore all this and insist on dating him anyway, bring your older brother, your eldest adult child or your protective uncle to the studio and introduce him. See what your family thinks, and remember: You'll never meet a con man you don't like.
Now me, I quit the business because I wanted to date my student. We're still together - but this whole dating thing was my idea, not hers. She turned me down the first time I asked her out; I had to feed her a few drinks before she'd accept a night on the town with me.