If that man had kissed me after a single dance I wouldn't have been half as nice as you were.
I actually think this here is the real center of the issue. OP is worried about being "rude" under these circumstances, and she's asked to be reassured that she wasn't, that in fact she was "nice" and "polite." But there is no reason why she had to be nice or polite to a drunk man who invaded her personal space. I'm not saying she had to scream "No, I won't dance with you, you drunk disgusting pig!" but she was in no way obligated to dance with or interact with this guy, any guy, at all.
Yes, you can refuse to dance with someone.
Yes, you can refuse to go out with someone.
No, you don't have to give reasons.
I sometimes go dancing with friends because I like the music and I like to dance, and since I'm married, I have no interest in dancing with anyone but my friends. When I get asked to dance, a simple "No thanks!" works. I've had a few guys be pushy and ask repeatedly, or demand to know why. "I said no, thank you" is a perfectly acceptable and polite follow-up. (This usually results in me being called a b*tch, not because I was impolite, but because they didn't get what they wanted and feel slighted.)
No matter how nice or polite a person is when asking for something, another person is not obligated to give it to them, be it a dollar, a date, or their dinner. And that doesn't make you "rude" any more than giving someone something that makes you uncomfortable makes you "nice."