Ooh, interesting question, I was talking to my partner about this very thing just recently. I’ll give it my best shot at answering.

Oh oh and this article is really good, not exactly answering your question but definitely relevant.

First off, don’t do it from a car, or in a way that the woman (I understand it may not always be a woman but for the purposes of discussion I’ll stick to the female example) is not able to respond to you. To have something yelled at you, however well-intentioned, and to look up and not even see who said it or be able to respond, is very intimidating. 

Some people find compliments from strangers very uncomfortable, whether because they’re wondering what the stranger’s angle is, or they find it hard to take compliments and don’t know what to say, or they think it’s rude that they should be able to go out without a stranger feeling entitled to judge their appearance (even if it is a nice judgement). I personally am okay with it: it makes my day when someone compliments my outfit (it is very often my shoes, I like wearing exciting shoes xD). But not everyone is in the same position. 

Also I guess we have to consider what your aim is: are you flirting with the girl in like a bar situation? Or are you on the bus and you just really like that girl’s hair and you want her to know that, for example? If it’s the flirting example, I advise to strike up conversation with something neutral, or if you start with a compliment, stick to complimenting her outfit, shoes, or maybe her hair: stay away from body-related comments, like how good her ass looks in that skirt (which in my book is a big no-no, to say first off). I think that maybe hair and clothes compliments are safer because, like, they are something that the woman has worked on? She spent time putting the outfit together or doing her hair: your complimenting something that in a way she can be proud of. Coz saying something like, “you have nice [body part/s]”, I automatically default to the reply, “thanks, I grew it/them myself” xD

I respect your comment about “Obviously, I’m taking it as given that she has every right to ignore me completely”. There may well be situations where you do try and compliment a woman and she takes it badly. It sucks to be rejected, and there seem to be a lot of examples of guys losing their temper when their advances have been rejected, to the point where women are scared to say ‘no’ in case their flatterer flips the fuck out. Understand where some women are coming from, whether it is very low self esteem, or a history of manipulative partners who have used compliments as a way to get what they want, etc etc. 

Unfortunately I can’t say what to do and what not to do (apart from the very obvious examples), because it is an entirely situation-dependent thing. You have no way of telling if your compliment will make a girl’s day, or ruin it. Your question shows you have a high level of awareness of the issues, and common sense, so I guess all I can say is use your best judgement depending on the situation. :) I hope this helps somewhat, and isn’t all just obvious stuff you already know. Thanks for stopping by my inbox! :)