What does the bible say about a married man or woman asking another married man or woman to dance with them? Is it wrong to dance with someone other than your spouse? Please provide scriptures.
There are no scriptures that deal directly with your question. The reason for that is that the idea of men and women dancing together is a relatively modern one. Throughout the times that the Bible was written it appears that men never danced with women. This tradition continued in Orthodox Judaism and others even into the twentieth century, and is still held by many Jews and Christians.
The only consideration I see in whether it is wrong to dance with someone other than your spouse is what your spouse says about it. Since there is no clear ban on it, or authorization for it, then is it going to cause division in the marriage?
The only passages I can find that might apply would be these. “Wives, submit yourselves unto your own husbands, as unto the Lord.” (Ephesians 5:22) “Husbands, love your wives, even as Christ also loved the church, and gave himself for it.” (Ephesians 5:25) “Wives, submit yourselves unto your own husbands, as it is fit in the Lord. Husbands, love your wives, and be not bitter against them.” (Colossians 3:18-19) These passages say that a spouse should consider the wishes of the other along with their own. It works both ways. On a question like this, both spouses should discuss it if the situation might arise.