Maybe!

But from a male perspective it still seems to be the case that women dont actually do much "searching". They wait for the man to make the approach. And that's regardless of the numbers against them.
*Sigh* hehehe
I guess we're sensitive souls and the reason we ask less is precisely the 'numbers against us'
10 guys at a milonga, 1 girl - she's not going to be refused a dance.
1 guy at a milonga, 10 girls - she's got more chance of being refused as he's got more choice.
I personally would probably dash to the toilet to have a moment if someone refused me. (I have never refused
anybody a dance,
ever...
mind you, for my own wellbeing I wish I had have done at times). As for making yourself available where there is no universal 'non verbal method of invitation'... pretty difficult. We can
assume that looking attentive and interested in what's going on on the dancefloor may mean you're more likely to get an invitation. BUT isn't that just a coincidence? Seeing as other posters have said no amount of non-verbal hinting that they were avoiding dancing put some men off from asking.
... actually, all this is making me prefer 'non verbal methods'. As I said, I did it once at salsa but picked my moment carefully. I don't know whether I can find my balls enough to replicate the moment, either in salsa or tango.
... even notice my rather indelicate turn of phrase re finding the chutzpah to be the
intiator of a dance. There's no getting over gender differences on or off the dancefloor... I think it's quite ingrained in women to sit and wait.. man is a hunter after all - we are the gatherers...
... on the other hand, I often find that men make really good followers - where does this come from? Men geared to following a general into battle unquestioningly? Hmmm....
Interesting stuff.
And as to the word 'available'.. it's roots are actually in Middle English meaning 'to be strong'.. funny how meanings change as it's connotations now seem to be 'passive/ waiting'...