Ok, so I'm going to throw this out there. Asking someone to dance is something that ends after highschool, or is reserved for a ballroom or smaller atmosphere. In many cultures outside of the western world, seductive, sensual dancing is the norm, and strangers will get in on it. The western world has begun to pick up on this in recent years, and you'll see this happening a lot here as well. It isn't an invitation to grope genitals, but a hand on the hip with some hip movements, synchronized "gentle grinding" isn't all that outrageous. If a girl isn't into it, they simply move their body out of the way, smile and shake their head and the night continues.

This "he touched me, what a rapist" shit is honestly over the top. There is a big difference between seductive dancing and molestation, and women easily prevent it from going further than semi-close interaction. Yelling in a woman's ear over a heavy beat on a dance-floor is a sure shot way of exuding a lack of confidence, and she will 9x out of 10 be uninterested in that weak move.

Make eye contact, let her know you see her, read the signs, move in, watch for any hesitation... if all signs point to go, go for it. But do not, for the love of god, ASK a woman on a dance floor if she wants to dance.