It is unknown where the term "Washer Woman" was first applied to women serving in the ranks, but it was an old term when we first have the first writing using the terms (During the Crusades when a camp was overtaken by the other side the first thing discussed was the exchange of the washer women).
Camp Followers were literally that, people who followed the Camp and thus were OUTSIDE THE CAMP. Washer Women were INSIDE the camp and as such an integral part of the Army. As to how many Washer women in any army is unknown, but each Platoon was entitled to at least one (Pre-WWI platoons generally had about 20 men to a Platoon). Thus a rough calculation was about 5% of any army was female (i.e. one out of at least 20).
The role of the Washer Woman was more than washing clothes. The Washer Woman brought the troops water when needed, cook the meals for the Platoon and general support for the Troops in addition to washing clothes (Through By Napoleonic times, Male cooks were doing a good bit of the Cooking, but a lot was still done by Washer-Woman). How most Washer Woman were selected is also unknown, but most ended up being the wife of the Platoon Sargent (And often hired together). In many ways a Platoon from the Time of the Crusades to the 1880s was like a Family, The Sergeant was the Father, and the Washer-Woman was the Mother (and often their son was the drummer boy). Please note, these are how things occurred, but other arrangements could be made i.e. hiring single females, hiring someone else than the Sargent's wife etc). The position of Washer-Woman was independent of her spouse in theory, but often not in practice.
At Company level the First Sargent ran the Company with its 3-5 Platoons (anywhere from 80-100 men and thus 4-5 washer women). It was NOT uncommon to find out that the First Sargent was the father or Father-in- law of the 4-5 Sergeant's in the Company (and thus the Father or Father-in-law of the 4-5 Washer Woman in the Company).
During the post-Civil War Era when it was decided that the meals of the men had to be "improved", it was decided to go with male cooks so they could go to cooking schools instead of staying with Washer Woman. Congress, like most other Governments of the time Period, decided that it was better to educate men to cook then to pay for the education of married Woman (Which most washer women were). In compensation enlisted men were permitted to get extra rations and pay for their spouse, but no education for their wives.
Just a rate about people who confuse Washer-Women with Camp followers, these were two different group of women. One subject to Military orders (The Washer Woman) and one outside those Rules (The Camp followers in most cases).
For some information on Women in the American Revolution see (and even here the Writer confuses Washer-women with Camp Followers, but if you look at the quotes from the reports of the time period, you will see the quotes do NOT make the confusion):
http://www.continentalline.org/articles/9501/950101.htmRegulation of the ConfederatE State's Army (# 121 addresses Washer Woman). I regret not having a better site, but Washer Woman are rarely addresses in military volumes or reports, they exist like the sky and the sun, and like the Sky and the Sun unless the washer women had some outstanding role in a battle are just assumed to exist and as such NOT mentioned.
http://www.geocities.com/capitalguards/CSARegs.pdf