Tom k, Philmont is a long hot dusty and sweaty trek. You will want to bathe and launder clothes as often as possible.
Everyone should carry their own small bottle unscented biodegradable soap (Campsuds) for personal use and a 2-gallon freezer-grade re-sealable plastic bag (washing machine) to do laundry in and 25 feet of 1.5 mm light reflective cord (Kelty Triptease) to air out your sleeping bag daily and for a clothesline.
You should only carry and wear 100% synthetic fiber clothes, polyester base layer T-shirts, nylon hiking shorts and synthetic blend socks and you should not have a problem drying them.
To launder clothes, half fill your washing machine with only clear cold water to rinse out dust, dirt and sweat a few items at a time changing the water frequently disposing of it in the Camp Sump. Then wash using Campsuds in the same method as before. Then rinse using the same method.
I usually wear my T-shirt and shorts to dry them, body heat drives moisture to the surface to evaporate. But socks must be line dried. Carry safety pins to hang them. I keep one pinned to the top of each sock.
You can give yourself a sponge bath using your washing machine, bandana and Campsuds. Its big enough to soak a foot in.
In a pinch, I have worn wet socks to bed in my sleeping bag. Surprisingly they dried rather quickly. They were cold and very uncomfortable at first but warmed up quickly and felt good shortly, go figure. But I would not normally choose this method for drying socks. LOL
“Philmont should be enjoyed, not endued.” Moonshine