First, the necessary caveats:

The West is the largest region of North America (being roughly half the continent). This enormous region includes many very different environments that resulted in different economies and settlement patterns: Historians of the West are often inclined to speak/write about "many Wests."

And ... the "Wild West" is a near-mythic place that is best visited in dime novels and in westerns in film and TV.

In general, a single woman had many options. The cliché of sex workers being the first to arrive in a western town is flatly wrong, but sex work was always an option. Because there were often many things a woman could do with herself, sex work was one of the least attractive options.

Mary McNair Mathews wrote a book about her Nevada sojourn during the 1870s, and I counted six different occupations that she pursued - often simultaneously: dressmaking, professional child care, teaching, taking in boarders (which included cooking), laundry work, and nursing - and she ended up owning rental properties. She even earned some money telling fortunes, although she regarded it as a lark and indicated that she did not believe and that the pursuit was less than desirable.

Because women often pursued several income-producing roles at the same time, what women were doing is often clouded in the census and other records. A man typically did one main thing to make money, and it was easy for him to tell anyone who asked what he did not a living. A woman often had to pick one of several possibilities, and given the standards of the day, that was often "housekeeping" (a "respectable" thing to declare) even though she might be doing other things as well.

There is even a reason to question the careers of sex workers: often a woman in a brothel might declared something like "milliner" or "dressmaker" to a census enumerator. We often interpret this as a way to avoid confessing sex work, but it may be that she made hats or dresses on her "off hours."

Because it took a while for a gender balance to be achieved in the West, a single woman was in demand socially. If you want to be married, you would literally have your pick, since there were typically a number of candidates for any single woman. A woman who wanted to be regarded as respectable would reserve social activities to church functions and to social events that were public and with proper monitoring for civil conduct - but there were always lots of opportunities.

There were, frankly, a lot of options for women - single or otherwise. Western territories and states tended to have liberal divorce laws, property ownership rights for woman, and were some of the first places to grant voting for women on the state level. There were social guardrails that restricted everyone's life - man or woman - but in many ways, the Old West was one of the better places/times to be a woman when it comes to options of various sorts.