If someone introduces a foreign guest to you at a foreign ball, you must ask her to dance with you, because it is impolite to refuse to dance with others on social occasions.

If you don't dance well, you can ask the partner if you want to sit for a while or not to dance.

At a dance, if you want to invite a foreign guest to dance, you can walk up to her and bow politely, and say, "can you dance with me?"

At a formal dance, if she wants to dance with you, she will tell you when you want to dance.

If there is no program, she may stand up to dance with you, or she may say, "sorry, I have a previous engagement."

Or she would say politely, "sorry, I don't want to jump this time."

At this point, you can judge her from her attitude. She may not be willing to dance with you, or she may be tired. She just wants to take a break. You should decide your own way of looking at your camera.