Obviously, this will depend on who's speaking and their agenda, as has been discussed in the thread. Those who are well-disposed towards her or polite will say "unmarried lady" to her face or to others. Those who are a little less polite might call her "unmarried" to her face but refer to her as a spinster to others. Those who are irritated with her or ill-disposed towards the concept of unwed ladies might call her "spinster" or even "old mai"d to her face. Even though "spinster" wasn't necessarily derogatory, it also had all kinds of social baggage to go with it. "Old maid" would be derogatory.
But then there's the fact that marital status is unlikely to be discussed up-front (because of the "social baggage" I allude to above). Again, politeness and attitude become a factor. A polite person would probably not allude to her unmarried status, either because it's a bit like pointing out that she has a big birthmark on her face (just a little embarrassing, oh my) or out of pity (well-founded or not). Or maybe they know her well and understand her situation, in which case they wouldn't bring it up at all. Someone who wants to take pot-shots at her will bring it up, or allude to it in a snarky way, most likely indirectly. Only someone quite rude would flat-out confront her with being a spinster to her face.
Oh, and social status is also a factor. If she's a woman from a good family, then of course people will be much more polite about the fact that she's unmarried, if only for the sake of her brothers and parents. Being unmarried, she is assumed to be a burden on her family, but if her family is comfortable, then that's less of an issue. If she is from a less well-off family, then there's less leeway, in part because she's assumed to be a burden on a family that perhaps cannot take the burden--and partially just because of class.
FWIW, I have a (very) minor unmarried woman of about thirty (my age!) in my Civil War WIP. We get reactions to her spinsterhood from a 13-year-old boy and his older, widowed aunt. They both refer to her as a spinster in exposition but not to her face. The boy finds her an oddity, and the aunt is condescending (and also super pissed because this spinster woman has sent the boy out into a battle). But this is subtext and exposition; the dialogue doesn't address it directly, even though the aunt/widow is spitting mad.