It's a faff, but I don't have a particular problem (other than finding somewhere sensible to put my glasses) stripping down to a sports bra at the side of the road in order to remove a baselayer, or for emergency bee extraction. Obviously it's not ideal next to a bus stop full of rowdy oiks, but if there are oiks around, there's probably a loo or something.
YMMV, of course; some people have scars they're self-conscious of, or have had bad experiences, or whatever. And it's obviously not a good idea in the sort of countries us QUILTBAGs tend to think twice about visiting in the first place.