Everyone loves being approached, generally speaking. Give a cursory check for someone who looks intent on not being disturbed, and otherwise go ahead and give it a shot. All the more "showy" signs of interest (smiles, hair twirling, winks, etc) can be mistaken or unintended.
The number one reason why approaches fail is that they never happen.
There is no safe way to know whether someone is interested or attracted before you make the approach. There's also basically nothing to lose.
The idea that women want to reserve flirtation to a small minority of men who meet certain explicit criteria, that they send clear telepathic signals to in advance to confirm assent is… a crazy myth.
The number two reason why approaches fail is that they "don't go anywhere" after the initial ice is successfully broken.
The only reason why pickup artists have any "superpowers" in terms of approaching and getting numbers from/dates with women, is that they practice incessantly, approach everyone they're interested in, and have a plan. It doesn't need to be elaborate, or a misogynist NLP hypnotic trick.
Just have a few good stories saved up, a joke or two, some upcoming events you can mention or even invite her to, and the ability to genuinely listen. That's it! Oh, and the 3 second rule (approach within three seconds of noticing her/making eye contact for best effect) is pretty good, too.