I used to go spelunking in my younger days – you’d come out of a cave with your coveralls caked with mud and crud and often soaking wet. Since most of the caves around here (PA and WV) were deep in the woods. it was often necessary to change to dry clothes right there, and always before getting back in the car you arrived in. Often I was the sole female on those trips.
I learned back then that trying to make a big deal out of modesty, struggling under towels or ponchos or trying to hide behind bushes, just prolonged the operation and tended to attract more attention. My modus operandi was just to strip down to my skivvies or the buff quickly and whip on my clean clothes with as little fanfare as possible. I once engaged a guy in a deep conversation about the geology of the cave we had just explored and performed my quick change while we were talking, never breaking eye contact. Not long after I was fully dressed he suddenly paused, looked kind of surprised and said “were you just naked and I missed it?” “Yup” said I.