I am a Swiss male who also likes to dance disco fox in clubs/bars occasionally. I have been in similar situations like you are in now.
I usually only do it with my friends with whom I was taking dancing classes with, so I know that they can disco fox.
When we dance, it is not because we have romantic interests - it's just for fun. But as you point out in your question, people don't know that. Partnerdancing in such locations does indeed come across as though you may be partners.
When I see two people dance like that, I am never going to ask the girl for a dance for two reasons.
1) If they are in a relationship, I think it would be quite rude
2) Dancing like that is quite exhausting and they probably want a break.
This is why it is up to YOU to ask strangers for a dance.
But all this is probably not news to you, since you are asking "how do I do that" and not "should I..".
So here are some tips that you should keep in mind for the next time you want to ask a stranger for a dance:
1) "I'm quite sure she would be fine if I just prompt someone else."
Make sure your friend is okay with you dancing with others. Don't just assume - ask her! Discuss the possible outcomes and ask her (and yourself :P) whith which of the outcomes she would be okay with
(partnerdancing with a stranger can be a bonding experience and is considered to be a very attractive feat by many people. It can lead to the new acquaintance wanting to stick with you the rest of the evening)
2) Ask your friend not to stare while you ask strangers for a dance and also while you are dancing.
This is very important to your actual question. The stranger probably has already noticed you two dancing. If your friend is watching / staring at you it implies that she is either your girlfriend or at least interested in you.
Not only is this part very crucial, it will also be quite difficult for your friend. As a learning dancer you automatically want to watch other people dance. Explain to your friend why you want her not to watch, it will make it easier for her and it stops her from thinking that you dont want her to watch for other reasons (shame, unspoken feelings, you 'picking up' other girls).
3) When asking people for a dance, be friendly and smile genuinely. Don't ever look at your friend.
4) Not all people can dance disco fox. Since you are a male and therefore in the leading position this is less an obstacle. I have danced with many girls that don't know how to disco fox. If they sound interested but say they can't dance,
Ensure them that it is no problem at all and it would be still very fun. If they do not sound/look interested, don't push it and ask another girl.
5) Do not mention your friend at all. Clarifying in any way that she is not your girlfriend would come off a bit strange and she will ask herself what she really is to you.
So how can I prompt someone in this situation to dance, while clearly
verbally or nonverbally expressing my partner is totally fine with
With the aforementioned points in mind you could approach strangers like this:
"Hey there! [smile, eye contact.]
I noticed you watched me dance
before. Would you like to have a go?
[hold out left hand palm up,
She will then most likely glance at your friend. This is why it is crucial for your friend not to stare! If the new acquaintance sees your friend doing something else and not looking at you, it will indicate that your friend is totally fine with what you are doing. (your friend not being in sight would have the same effect)
A more gallant way of asking would be "Would you do me the honor?" instead of "Would you like to have a go?". Of course there are many other variants, you will have to evaluate yourself how exactly you would word your question based on your personality and the type of the disco/bar and the stranger herself.
More important is that you smile genuinely and stay friendly. Eye contact never hurts, too.
sidenote: after reading this again I realized that it could be possible for your friend to actually look, but with a smile! Her smiling would be the ultimate indication of "I'm happy with that".
- make sure your friend is 100% okay with you asking others for a dance
- tell your partner not to watch (or if she does, she should smile)
- simply and friendly ask strangers for a dance
- do not mention your friend
Sorry for the long and sidetracking answer. I hope it helps though ;)