At my studio, there's a sort of unwritten rule that people change partners for every dance or at most dance two in a row. I've had some success with overly persistent guys by reminding them of that (some have been too clueless to have figured it out themselves).
Otherwise, your girlfriend will just have to be a bit rude to him. She can decline a dance with something like, "Sorry, not now, I want to spend some time/dance with my boyfriend." If he's in your seat, she can say "Sorry, that's my boyfriend's seat" if he doesn't get up when you come back. The operative word is "boyfriend" (even if you don't use that word yourselves, it the best for getting the point across to someone clueless).
If that doesn't work, she'll have to be blunt. I have heard of some women in that position who actually give these guys a "quota," like "I'd be happy to dance with you X times a night, but not more." Or she can just start declining all the time.