I think I always ask the lady to dance, no matter what company she is in or what she is doing; I also leave it up to her to wrap up any conversation (assuming she accepts my smile and offer of a hand as invitation.)
If her back is to me I will touch her shoulder first, but I assume that she will make her own excuses with the company she is in.
(I'm not a very vocal person; dancing is tactile and expressive with lots of physical signals and body language - who needs to talk in such a dinn?
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