I used cloth diapers with my babies so I also had "cloth wipes" or little 3" X 6" washcloths for washing the baby's bottom (i've had these wipes for a long time, some 17 years, some 13 years).
I don't have a baby in the family right now, but we use these wipes in our bathroom. I keep them loosely tossed into a small metal waste basket next to the toilet. Also, I have another small metal garbage can with a lid that opens with a foot pedal and has a bucket inside. I line it with a mesh garment laundering bag.
Family members (often, not exclusively) use the cloth wipes instead of toilet paper by taking a clean one out of the waste basket, using it (either dry or after wetting it at the sink), and then putting it into the mesh bag inside the closed garbage can. (I got both containers and the small mesh laundry bag at Walmart).
When the waste basket of clean cloths is empty, or almost empty, I open the lidded garbage can, take out the mesh bag, zip it up, and wash these little cloths inside the mesh bag in the washing machine with underwear etc.
It's really not inconvenient. I don't do extra laundry because we are using these cloth wipes in place of toilet paper.
Although toilet paper is still available, we could do with out it if we had to, especially when no "BM" is involved in the toileting. Even then, we are used to this system, and it really isn't more unsanitary than using toilet paper, which is thin, easily ripped and definitely not a secure system for keeping bodily fluids off of your hands. As long as we wash our hands well after using the restroom, using cloth doesn't affect our health.
Of course toilet paper is easily biodegradable in our septic system. But, it's made out of trees, and I'm thinking there's no reason to use it if we actually don't have to. When we're sick with a digestive illness of some kind, then we use toilet paper and flush those real germs away as a precaution against the laundry doer accidentally being exposed to them. But we very rarely get sick in our family, with any kind of illness. So, the rest of the time, people in my family often use the little washcloths.
Some are flannel, some are terricloth and some are a combination of both. They all work great for what we're using them for, and help us reduce toileting related consumer waste to zero.
We also use cloth wipes for ourselves at home. We keep them folded in a basket on the toilet. And the wipes never stink or are gross! Simply because we clean ourselves with water (using a watering can) before drying, which is all the wipes are used for, drying the water, not icky stuff. Then we placed the used wipe in a small wet bag which was left over from cloth diaper days :) Hygenic and no waste!