Alice:
My boyfriend is also a dance instructor and has been for many years. I know how hard it can be.
You have to have faith in him and trust him. I know it's easier said than done, but that's the case with any relationship.
Remember, this is his job. In my case, it also happens to be my boyfriend's passion. I've never doubted him. I trust him completely because I know he is a professional. People have asked, "Doesn't it kill you to see him with other women?" Sure, it's hard sometimes. But, all he's doing is sharing his passion for dance with others (and making a living to support his family).
Have you tried taking lessons and sharing his passion? I think that's helped our relationship. Don't get me wrong, taking lessons from your significant other is a HUGE challenge, but it's so worth it. I love dancing with him and I understand why he does what he does.
If he's never given your reason to doubt him, then you shouldn't. If he's a man of principle, then he would never "date" a student or be untrue to you.
Good luck to you! And, go dance with him!!