Women engaged in sexual commerce in the West during the nineteenth century were far rarer than the cliché and some novels and poorly-researched histories would have us believe. I worked extensively with the Nevada portion of the 1860 federal census, seeking the proverbial first women=prostitutes in Virginia City and Gold Hill, both of which were first established in 1859. There were over 3,000 residents in the two communities, with 111 women 16 years or older. Of those women, none appeared to be prostitutes. One must use source criticism because prostitutes often lied to census enumerators, but these women were wives or daughters in families or they were claiming occupations that seemed reasonable.

The fact is, a woman who was newly arrived in a prosperous mining district did not need to rely on sexual commerce for a living. Baking bread, sewing clothes, or any number of other things could result in a great deal of payment, so even a prostitute from another place would have every reason to give her body a rest and make lots of money doing other things.

In addition, it appears that prostitutes used a great deal of caution about relocating from an established venue before relocating; everyone knew that a new mining camp could fail, so there was no reason to relocate during the early part of a boom, only to have to undergo to the expense and bother to relocate again. Prostitutes began arriving in Virginia City by 1862.

But what of their numbers? The 1870 census documents what were probably the largest number of prostitutes. With a great deal of combing through the records to find as many women as possible who were engaged in prostitution, I was able to count no more than 200, in a community with several thousand women. By 1880, their numbers had declined while the number of women in general dramatically increased. Prostitutes were always a minority. Marion S. Goldman in her Gold Diggers and Silver Miners: Prostitution and Social Life on the Comstock Lode (1981) claims prostitutes were the largest occupation group. This is clearly wrong. First of all, "Keeping House" was itself an occupation, which far outnumbered all other occupations present in the census records - combined. And primary sources clearly indicate that most of these women, while claiming "Keeping House," were engaged in many money making enterprises. That said, the census listing of female servants outnumbers prostitutes, so Goldman had no basis for her claim.

I discuss this in an article I wrote for a collection of essays I edited: Ronald M. James and C. Elizabeth Raymond, Comstock Women: The Making of a Mining Community (1998).

In addition, I had occasion to ask two noted histories about the folklore about the first women in mining towns being prostitutes. Sally Zanjani, the leading expert on Goldfield, Nevada and Mary Murphy, a gifted historian of Butte Montana: both indicated that they had looked at this question in their own research domains and concluded that the first women were not prostitutes. I realize that your question is about numbers in general, but it seems clear to me that from beginning to end, prostitutes were always in a small minority.

edit: minor clarification

Itsallfolklore is most likely right. Sounds as if he did his home work. I guess we would have to consider what you call "the old West." I lived in Montana in Great Falls. Some of the old timers could point out buildings and the local paper often had stories about buildings that were bordellos well into the 1940s.

In Great Falls I was visiting in one neighbor hood of some of the original homes of the town. Very nice, rather large, multi story homes. Between two of them was a long but narrow very basic single story wood building.
I thought it odd for no bigger than it was that it had four doors on one side. The man I was talking with told me it was a "crib" from the old days. I was also a hospice volunteer and one day I took an elderly man out for a drive. He had been raised in Great Falls. He seemed to take delight in pointing out where all of the old bordellos were. I guess I knew what he spent most of his youth doing.

In Butte Montana's hey day an entire city block was whore houses. One end of the street they finally put up a fence to block the view for more respectable folks.
One of the places was built to be a whorehouse and managed to stay in business up until the 1980s. Though it was against the law it was a well known secret and in plain view.

According to a film I watched in the Albuquerque museum, the Duke city had more brothels, opium dens and saloons than any other town in the west, in spite of it's small population. Being the intersection of the Santa Fe trail, the Santa Fe railroad and the Rio Grande river it was a nexus for travelers of various types, and accommodated the demands of cowboys, cattlemen and other temporary residents.