First off, Its not AFC to tell people your name or ask people for there name. Try opening with, "Hey I'm _______." It works amazing.
I'm guessing she checked you out ("looked at you") and thought you were cute ('smiled" and then "gave me a punch and handshake") and wanted to dance on your dick. She did, but you ended up walking away.
You dont need a verbal opener on the dance floor. You dont need to talk. Its all LAZER EYE CONTACT and LEADING.
btw your in luck, cuz I got these photos of me in the club last weekend. I opened a chick dancing on a table. I like to play role-reversal, so I pretended I was a girl grinding on her for a sec. Grabed her hand and made her slap my ass. Double hand spin her around, closed the distance. and made out.
NOTE: I did not THINK about doing this when I was appraoching her, I just did it because i FELT like it.

I just hopped up there, tap her, and grinded on her.

She's slapping my ass (sorry I didnt rotate the pic).

Double hand spin

Closed the distance for the lazer eye contact and makeout.