Sorry for chipping in here, but I had the same worry but in reverse a few years ago so thought I might be able to help.
Do you have self service checkouts in America? All most all supermarkets do here in the UK and that's how I brought my underwear because there doesn't have to be any interaction with other humans.
When I lived at home I either had to handwash in the sink, just chuck some washing powder/liquid in and rub things around until they're clean and rinse well. Make sure you have something to carry them out of the bathroom in if someone's likely to spot you carrying them back to your room, I forgot once and putting wet underwear on to smuggle them past parents wasn't a fun experience! I dried them by hanging them up in the hottest part of the room, which shouldn't take long if you have heating. If I knew everyone was going to be out for a while I'd use the 15 minute cycle on the washing machine to speed things up.
