I think you should probably ask her out after a few more weeks.. you don't know exactly how she's feeling, and if her last relationship was something that was going on for a long time, then she might be really sensitive/depressed about the breakup. Since you see her at school, just hang around her a bit to make sure she's feeling a little more comfortable around you and what has happened to her already, then it might be alright to ask her out. If you really like her, then give her a chance rather than this other girl who you never talk to but think is pretty..
Also, about the dance thing, I would say no. Awkward. Why would I want to suddenly dance with some guy, (despite the fact I would be thinking he was cute) without music? Pretty pointless, and weird, in my opinion. Hope this helped.