Keeping clean is a good thing. You can go for long periods without bathing --that much is true. But you can also keep your standards, or even raise them.

You don't need rivers or lakes (but you can use them when available, though it is most responsible to use soaps away from them, and even then to use biodegradable products) or showers. You can use water bottles, 1.5 liters for better capacity. The squirt tops are useful (for shampooing, among other things). You can sometimes find warm water to fill them with, or leave them in the sun for a while.

It also helps to be able to use cold or cool water happily. (After learning to do so I found this to be very liberating.)

A good compact microfiber towel is a godsend. These things are great. You can even find them in earth colors if you look around.

A small squirt bottle for the soap is handy if you are using liquid soap like Bronners (the smaller sizes of which come in just such bottles).

Microfiber towels are also good for sponge baths. They clean very well even without soap. Not kidding -- you can find studies online.

The other thing I have found to be very useful and effective is a spray bottle (mister, atomizer). Extremely useful. Just spray your face for example, or your hands, and then go over them with a microfiber towel, drying and cleaning at the same time. Very effective -- more so than you might expect.

These sprayers are also efficient -- good for conserving water. This can be useful, make it last, and save weight.

And they have many other uses as well -- showering, freshening up, cleaning various items, washing apples, pears and other fruit, etc.

A quick mister shower can be taken in a tent before going to sleep, and helps keep the sleeping bag clean. (I also find that I sleep better when clean.)

You can also mist the nylon fabric of a tent or sleeping bag (also certain clothing items and stains or spills) and then dry/clean with a microfiber cloth. Good for spot cleaning, freshening, and touching up.

These misters come in various sizes and spray patterns. You can find them all over the place. Dollar Tree sells body sprays in small misters that you can just empty out and use. The various misters sold for hair care and barbering can work. Cleaning and car care products come in useful spray bottles, as do many other products. Some salad dressing spray bottles are good. There is a wide array to choose from.

The Travel Bottle Kits at some stores (including DT) sometimes contain a good, compact mister bottle, along with some other small and useful containers. Good kits.