Okay, I'm going to engage in the futile exercise of trying to make sense of that train-wreck of a film.
Here is a possibility -
Nomi is working in a strip club, yes. But she doesn't especially like it, she doesn't like being treated like an object, and the dream of being a "showgirl" is based on the belief that it's a more classy, artistic endeavor based on the pure dancing talent one has.
There's nudity, yes, but not the "shake your boobs," prurient, objectifying kind (in her mind, anyway). It's like the difference between a painting of a nude by a classic artist, or an ancient Greek sculpture vs a spread in Penthouse Magazine.
So, if she's a fantastic dancer, and this is the high-art, classy undertaking she's dreamed of, then she'd be chosen on her dancing talent, with the understanding that she'd have to show her body as part of the show.
It's the difference between being a dancer who happens to be nude, and a pair of breasts being displayed under the pretense of a dance.
There's really no reason for her to need to show them in what is supposed to be a dance audition that supposedly focuses on talent, so it's that much more objectifying to have to display herself, unexpectedly, for the jollies of the guy in charge, just to try and get her dream.
It's the realization that her dream, as she always thought of it, doesn't really exist and what she's chasing isn't that far removed from what she's put herself through to get there. What she's running to is way too similar to what she's trying to escape and that realization hits home in that moment.
Or maybe it just seemed a little more dirty if she didn't want to show it. Who can really make sense of that mess?