Again, it depends. Yes, it's not their milonga; they're out to enjoy themselves. They can dance with other maestros, or not at all, or whoever they choose. But maybe it's the studio's milonga; a showcase for the business; an intro to milonga for novice students. It's trickier when you're learning and the instructors don't show the way.
Paid dances and taxi dancers have been given an undeserved bad rap in tango.
Active is good, in my view. The thing to avoid is "buzzing around" (as my partner would put it, "ne sois pas une mouche"). If you're going to invite, either use a firm gaze from afar or – if verbal invites are fine for you – walk up from afar, ask, and then either dance or leave. But it's the kiss of death to kind of loiter nearer and nearer by, hinting but not asking. That gets very annoying very quickly.
That's regional. Here, your odds at the smaller milongas would be poor, because small milongas are small due to being the domains of cliques that don't open up much. Big milongas are hotbeds of "What the heck!" invitations shot across a room in a moment of clear sightlines. People know that in a chaotic mob, if a tanda doesn't work out, they're unlikely to be spotted being uncomfortable while dancing among 50 other couples three lanes deep, and they'll have a crowd to hide in afterward.
That's regional, too. Most of the more liberal inviters here are very, very experienced. They can dance with anyone – and while they are burned out a bit, it isn't with tango but with the same partners. So, if a new face shows up, they're happy to see them and capable of dancing with them.
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My experience is men seem to have no trouble, but I have often seen visiting ladies (both in my little area, and when I have travelled) struggle to get dances, particularly the first dance. It doesn't seem to, but I think the thinking should go like this: "There is a new lady I have never seen before. She has the right uniform (knee length dress, Tango shoes). She seems to know the codigos. She looks to be in good shape. She has the confidence to show up as an unknown at a Tango event. She obviously likes Tango. It seems like there is a good chance she is an above average dancer and it is worth risking the last 2 songs of a Tanda with her."
I find those steps just . . . wild. That's because of what you said afterward. My first few years of tango were characterized by changing areas that smelled like feet, coming home covered in sweat and studio dust, routine bouts of frustration leading to nearly quitting, and barely contained grumpiness at myself and at partners over things not working. By the time I was comfortable going out alone, inviting random people to dance, etc., all the "sexy" had been beaten out of it. At this juncture, I'd see a paid dance or a taxi dancer as something akin to anger-management therapy to avoid giving up in frustration, and nothing more.
That could be. I confess to having a leader's perspective. When a leader shows up to a place that has too many followers, it's seen as a good thing . . .
I've recently danced with several tourists (mostly from Eastern Europe, which is odd in Canada) just because they were sitting there and I'd never seen them before. If you're a strictly local dancer like me, and rarely go abroad to dance, dancing with visitors provides much of the fun of tango tourism at a fraction of the cost.
It occurs to me that this, too, might be far from universal. If you got into tango by some alternative route, you might look at it differently. I could totally see that affecting your confidence (or lack thereof) to attend milongas alone.
It depends where you are dancing. If you're dancing at a very traditional milonga in B.A., I'd say wait until they get to know you or see you dance a bit. If you're in North America or Europe, you can be a bit bolder in your actions. I'd keep trying to catch someone's eye so they cabeceo you; I'd do that before asking directly even if it takes longer. Maybe chat with people from time to time to break the ice and let them know you are there. If you can find one person to dance with you and the others see that you can dance well, things should get easier after that. Really depends a bit on the local scene by you.
There are many routes, and many personal issues, not forgetting imposter syndrome. Whilst I don't wholly subscribe to the old codigos, they had the advantage that you knew the rules - except role-based rules rightly changed.
Probably depends where you dance. I know there are women who are very proactive in that sense, especially if they want to dance with specific men for specific music.
Some of them do, even with someone new to the milonga. BA would have been more fun if I had the confidence in my dancing and my Spanish to accept.
In that case, you probably don't want to dance with most of your current dance partners in a year or so. And in two years you just won't do it anymore. It gets you down as they struggle and try to get their steps right. You're just not in the same boat.