Reel and Wheel
The art of asking someone to dance is a little researched subject. For many people, the standard "would you like to dance?" or "will you dance?" suffices throughout their dancing career. Some people never even progress that far, and spend their time at dances wandering the floor continually hoping to be asked to dance, or always ending up with the last person in the room as the couple which completes the last set.
On the other hand are the people with flowery speeches, who can spend so long asking you that by the time you get on the floor, the dance is over. On the shorter end of there are requests along the vein of "I think you are the most beautiful woman in the world - will you dance with me?" This can cause problems later when asking the lady next to her to dance. Then there are the more formal requests, such as "would you do me the honour of this dance?" These last ones are suitable on certain occasions, especially when you are hoping for more than a dance.
There are also the cautious requests... "Do you have a partner for this dance?" "Are you taken?" These have become more common since the start of booking dances, a practice simultaneously verbally condemned and enthusiastically practiced by many. This is a practical way of ensuring you dance all the dances you want to, with the partner you want to, but loses the spontaneous impulse of other requests.
There are also, of course, the non verbal requests - raising an eyebrow across the dance floor can be worth a thousand words. Providing the person in question is actually looking at you. Then there is the over-dramatic bow, the "loiter with intent," and even the dramatic jump across the dance floor, culminating in landing directly in front of the desired partner.
However, these all pall in comparison with the new heights to which Andrew Thomson has proposed to take requesting a dance. In the most direct fashion, the latest line is "Origh' darlin', get yer crib, yer've pulled."