Rejection is just a part of the game.
On this issue, I usually say "what's up?" and introduce myself and ask their name. Then I'm like "wanna dance?". Its so much easier.
Whoever is looking just sees you as talking to her for a bit and then you leaving. Plus I do this because its much better than trying to dance w/ the girl and then her moving running away and making a scene which makes you look like a fool.
I find this works for me because they get that I actually want to dance with them the "person", by asking their name. That's my pop psychology theory I guess. This change has worked a lot better for me. I dance w/ more girls than ever by doing this.
I see a lot of guys dancing behind the girls, sometimes for a really long time, almost sneaking up on them, then eventually grabbing them. I see a lot of guys get rejected that way with girls pushing them away or moving away. Girls know your there from the get go. Their friends know, there already letting the girl know.
However, from my experience it is ESSENTIAL, that the girls or the girl you want to dance with sees you dancing and having fun before you dance w/ her. You must already be having fun before you try and dance w/ her. If you are sitting on the wall or standing stonefaced and then suddenly try and dance w/ her its not going to work. She will pretty much see you as just trying to get a feel of her (which is part of that lol), or just weird.
If you are already dancing and having fun, she will feed off of your vibe and be more likely to dance with you.
Dancing w/ girls when you go out is so much fun, especially if you get a girl who can ance and who has rhythm. I agree there are those girls who just go to have their ego stroked.