The sink in your tent
If staying in a tent, just ask the staff to do you up a couple of pails of warm water....I would want better soap then the soap leaves. They got out the sweat of the day, but didn't remove any of the black marks from rubbing against the roof rack. Didn't worry about it though as the wildlife don't care what you look like. The marks came out when we washed the garments when we got home. Otherwise in the lodges we just used the sink......do make sure that you have 2 nights at the same place before you do your laundry as you will need the extra nights to dry.
You will need to wash your underwear yourself, so take some travel wash liquid.
I've read good things about the Flexoline latex braid laundry line, I plan to bring one with me to Tanzania. Also, a flat sink stopper, and some carabiners or clips to help hang things up. Also, it seems like a good opportunity to embrace not being particularly clean or fragrant for a while. Plenty of time for that after returning home.
With the international flight restrictions on liquids, and liquid soap's remarkable ability to escape from bottles at the worst possible time - dry laundry soap is a good option. I use it very sparingly when water is scarce - often just rinse the clothes without it.
But if you have enough water available, a nice gentle product like Woolite works great and rinses out more easily than some other soaps
I hate paying the premium for little packets... and the rest of the Woolite products seem to now be liquids... so next time I'll probably head to the baby laundry soap area... there are some products like Dreft powder advertised as mild for babies that should fit the bill... toss some in a ziplock bag and no need to pull it out at every security check.
You can take pure soap that is readily available in most supermarkets and it will wash both clothes and bodies so no issues with liquids.
What I would do apart from the excellent advice given above is when you are at a lodge or camp for more than 1 night on arrival ask about laundry, the cost and get as much done then as possible.
Some places will be expensive other not so ...others free...except for the tip.
A friend gave me this tip and it works a treat. After washing clothes and wringing them out by hand, lay them on a towel and fold the towel over the top of them and then stomp all over them. Your body weight will squeeze so much more water out than your hands are. Some items honestly come out feeling almost dry.
Dont lay washing over a bush or on the ground to dry, there is a nasty little bug called the Putzi fly, ( …wikipedia.org/wiki/Cordylobia_anthropophaga ) that just LOVES to lay its eggs on damp laundry. On contact with skin, the eggs hatch and burrow into the skin. Laundry washed by the lodge/camp is usually ironed to eliminate any eggs that may have been laid. As said in 3 above, underwear will not be handled by the staff, and after washing should be dried indoors unless ironed by the owner.
But there is no problem when you wash out your own things and hang them on a line in your room-even in a tented camp?