Try to convince her that the try-out isn't a test of her, but her chance to see if she likes dancing with the guy. Can you do the tryouts at your studio? She might feel more comfortable there. If you want to be sneaky, here are a couple more lies you could tell her:

--arrange for a tryout with a partner who is significantly below her level, so she can have the experience of being the better dancer and do the rejecting (hard on the guy, but she's your main concern). Of course, it might be good for her to be the better dancer in her partnership, so she'll feel more confident about dealing with the partnership issues that come up once she finds a partner.

--invite the guy to share a lesson with her. Tell her he wants to work on his connection or something with someone other than his instructor and you think she can help him.