I'm not sure why you didn't ask to see her again after your last dance together but that's water under the bridge now so yes, ask her out over instagram if she accepts your friend request and just say: "I enjoyed your company and the dances we had the other night."
Quickly ask her out for a drink or a pizza or to do something you both like to do once you get chatting.
Good luck.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion