You've seen my Pocket Kitchen for day rides; here's my Cyclist's Laundry for long tours...
It is illegal in many places here in the States (and a Really Bad Idea) to place or dump soap into a potential water source, whether pond or running stream. It kills fish, frogs and tadpoles, renders the water undrinkable for animals, and surfactants strip the oils that make duck and goose feathers waterproof. Doing laundry when wild-camping can be really problematic.
I came up with a solution awhile ago that has worked well in practice and takes very little room in my panniers.
I place my dirty clothing in a 2-gallon/7.5l Ziplock freezer bag (freezer bags are made of more durable plastic and seem to have better sealing at the closure). Dump in a bit of biodegradable soap and some water, and squeeze out excess air before zipping the bag shut. Let it sit -- preferably in the sun, but shade is fine -- for about 90 minutes, agitating the bag when you think of it. Afterwards, dump out the soapy water well away from any water sources (the middle of a dry gravel road seems to do the least damage). Fill the sack with clear water from your stores (or transferred from a source) and agitate again. Repeat once and the water should be clear. Even so, considerable caution is necessary. In some areas -- particularly in the desert or in fragile alpine locales -- the flora is just too sensitive to expose to soapy rinsewater, and something as innocent as Wash Day can cause some real devastation, so it pays to use real care. Still, this makes it possible to do laundry in areas where it would be difficult or unadvisable otherwise and is more responsible than soap in a stream. I make sure I use a phosphate-free biodegradeable soap intended to create minimal foam and to break down quickly.
Once clean, I hang my laundry to dry on a clothesline. I recently purchased one I like, the Sea to Summit Lite Line clothesline:
http://www.seatosummit.com/products/display/3 , reviews here:
http://www.rei.com/product/807452/sea-to-summit-lite-line-clothesline/showdetail.php?Code=ACLOTH It uses a captive pouch, two hooks, a line-loc tent-line tensioner, and twin lines with captive rubber beads substituting for clothespins. It is great; weighs just 1.3oz/36 grams and is 11.5ft/3.5 meters long (and can be doubled back on itself or shortened with the line-loc). Using the Click-Stand on Sherpa, I can tie one end to the seatpost and the other to my tent ridgepole if no trees are present. Otherwise, I can string it between the bike and a tree branch.
My Dutch friend prefers to use his roll-top Ortliebs as a washbucket. His method involves dumping in the dirty clothes, water, and soap, then riding around for a bit on bumpy roads. He dumps out the soap and rinses in the same pannier. I don't know how I'd get the pannier clean or dry again, but he packs differently than I do in my Ortlieb Packers. He says the procedure leaves the pannier nice and clean with a fresh soapy scent, but cautions one to use the pannier your pack clothes in, not the one for food storage.
I also picked up a $1 universal suction stopper so I can keep water in a motel basin or at least take a usable tub bath if the shower head fails. Most hotels and motels here remove the stoppers to prevent people doing laundry in their rooms and causing damage as a result. If I use my stopper and carefully place my clothesline over the tub or in the shower to prevent any drips on carpet or floor, I do fine. I like to leave the wild places as clean and untouched as I found them, and I do the same in formal lodging.
Best,
Dan.