Actually, good performers don't worry about messing up, it's all about the art and the performance and their love for it. I've known plenty of casual and serious dancers, and just going by the numbers, very few dance partners end up in romantic relationships. Most dancers know that it can make the situation too sticky. When you have a dance partner, you rely on that person to help you express your artform. A relationship can make that complicated, and even the casual dancers know this and avoid it. This is different from 2 people who are already in a relationship becoming partners.
So even though that might make you feel better, there is no denying the sexuality of dance. Yes, the male and female dancers sometimes have to hint at some deep sexual attraction/friction. But that doesn't mean it's actually there (hence the professionalism someone above mentioned). But if you're going to continue to date a dancer, you have to come to terms with that, no matter what.
In the end, trust her, go to her shows, and tell her how you feel about all this every once in a while without being whiny. Don't avoid her shows just because they make you uncomfortable, that will end the relationship. It's completely reasonable to feel the pangs of jealousy, just don't let it control you and it won't be the cause of a breakup.
