On a long trip you will wear your clothes much longer than when living in a house. We have several sets we work from, such as: decent or respectable clothes for eating out, shopping or when crossing a border; driving set which is usually just a simple shirt to keep cool with the windows down and the bottoms of the decent set (makes changing from driving to decent rather quick); camp set that usually takes the brunt of the most dirt; sleeping set; and usually one bathing suit. Over the years we have found that works best so we dress for the occasion but are always slightly under-dressed. Underwear and socks are what we go through the fastest, next are camp clothes, then sleeping with decent clothes normally not getting worn much at all. Hiking or sporting clothes are separate and pulled out for the exact activity and handled as needed. I will rotate my driving cargo pants in for hiking and pull a fresh pair out to replace them for my decent pair. Example wardrobe for him: decent - Short-sleeve button down and zip off cargo pants, driving - colored a-shirt or tank top, camp - a-shirt and sport shorts, sleeping - old sport shorts, and one pair bathing suit shorts. For her: decent - nice leggings/jeans/skirt and simple blouse or fancy tank top/tee, driving - normal or sporting tank top, camp - leggings/jeans/shorts and tank top, sleeping - long tank top or tee shirt (normally one of his), and one or two bikinis. We have a small reusable shopping bag that all of our working set of clothes fit in and it lives behind the driver seat for quick access. In the extra space in the bag, Mandi keeps a set of yoga clothes and a pair of pants if she is wearing leggings and at least one extra shirt so she can swap things as she desires. We also always keep out a sweater each to grab when it cools down at night or when we need to enter the arctic exhibit to purchase food.
As for washing we use to just do the bucket thing and hit laundromats as needed, usually self serve but in Latin America sometimes you have to get the full wash and fold at a per kilo price as that's all that there is available. We don't use fabric softener so that's why we prefer to do our laundry ourselves. We have picked up a Scrubba and use it over just a bucket as it does do a better job, we use the buckets to keep a steady flow of clean water and have a dirty water collector so we can dispose of it properly. In a pinch, we have emptied one of our large bins to hand wash bedding. It is a laborious job but you gotta do what you gotta do. Self-serve laundry is everywhere in the US and Canada so that's the best way to go. In parts of Canada and Alaska the laundromats also had showers so we were able to wash everything and leave all sparkly clean, some truck stops are set up similarly.
Under the bag of working clothes we keep a laundry bag to house our dirty clothes. We can gauge when we need to do hand loads or hit a laundromat by it's size. When we do hit a laundromat we wash everything. We prefer the big front loaders, we stopped separating clothes near the turn of the millennium, so everything goes into one big load. Many of our clothes are 'technical' or quick dry so we just hang those in the van and they air dry as we drive to our destination, everything else goes into the dryer. Obviously weather will determine the working wardrobe but this is a rough idea. We do carry 2-3 sets of each type of clothing but we were fulltime for a long time so we carried way too many clothes. We also carry full winter clothing so base layers, jackets, scarves, etc... Everything stays packed away unless we are in that particular season or environment.