Think carefully about the pressures of the situation. For example, a smile is usually good, unless they are on a job where they are made to smile by their employer.
Essentially, you are right that its inappropriate to approach somebody without business. But getting to know somebody is legitimate business.
You are also sort of right that it has to be an appropriate context for chatting. But it doesnt have to be explicit. If you cross paths in a public place, 1 critical factor is how quickly you are both moving. If she is hurrying, not good. If she is relaxed, that is good.
Pay attention to the other person. The other person is the unknown factor, so its alright to focus on understanding their perspective. And its never as simple as interested/not interested. Empathy is clutch here.
Attention is an offer. Some people, especially from sick cultures, can be really mean when they reject an offer. Dont take that personally, its really about how disappointed they are with what they themselves receive.
Or like mocking Moon colonization in 1970