I've been curious about the same sort of question. My experience so far is that the contra dance world pretends there is no ASCAP, and usually vice versa.
If you don't mind sharing, Rob, what kind of rates are they asking you for? Also, are they asking about your dance in particular, or about the venue? I had thought that an event couldn't really buy their own license; it has to be a license for the whole venue, for anything that happens there 24/7.