What was the price of a shot and a bottle of whiskey in the American West in 1870s roughly? For the end consumer, in a saloon, not wholesale.
The traditional price for a bottle of cheap whiskey in a cowboy saloon was two bits (25 cents). See the Kansas City Post Gazette, March 3, 1886, p. 6.
Hard drinks were not sold in "shots". They were sold in a small glass which normally held a gill (4 ounces) and cost 5 cents.
These prices could be much higher in cities or for name brand liquors. For example, a fancy bottle of brandy might be 3 dollars. A good quality bottle of whiskey in a nice hotel might be as much as 2 dollars.
There is a terrific site, Legends Of America. It goes into pretty good detail about the history of the Old West, including noted people and vices. In its discussion about the real Gem Saloon of Deadwood, South Dakota, owned and operated by Al Swearengen (made famous in HBO's Deadwood), it mentions that
In the front of the theater were a bar and many seat for spectators. The rear of the building held several small curtained rooms where the Gem's "painted ladies” entertained their customers. On its balcony, the Gem band was said to have played every night, while the girls beckoned to potential customers to com forth. Once inside, the women charged their customers 10¢ for a dance, 20¢ for a beer and $1 for a bottle of wine. As to charges for the "other," it remains unknown.
However the paragraph is not cited, so whether it is true or not remains to be seen. There are many photos in the site of saloons. Perhaps studying some you might be able to make out price lists above the bars.
I would agree, however, with Tyler Durden's assessment. It stands to reason that a so-called "shot" would have been priced somewhere between 10 and 25 cents, and a bottle (of rotgut) would have been $1 or so. That would be extremely watered down though. A bottle of the "good stuff" would have been correspondingly higher.
Western nineteenth-century saloons were traditionally identified as single bit or two bit saloons: i.e. they either charged a single bit (12.5 cents) for a beer, a glass of whiskey, or a cigar; or they charged twice that amount - 25 cents for each. Customers at a single bit establishment could pay with a quarter, and they would receive a "short bit" - or a dime - in change, which could then be used for the next round. Elliott in his important book on Rocky Mountain saloons also talks about half bit establishments, but that would have been offering a product for too low of a price for most communities.
Dan DeQuille (William Wright) in his 1876 book The Big Bonanza tells a story about a customer who came into a two-bit saloon, drank a glass of whiskey, and then offered a short bit in payment. The bartender objected at explained that it was a two-bit establishment at which the customer said that this was his understanding until he tasted the whiskey, which seemed to warrant only a single bit.
On this, see Kelly Dixon's work, Boomtown Saloons, or Ronald M. James, Virginia City: Secrets of a Western Part (2012).
In the very early 1900s in Alaska (gold rush era), "real" liquor went for about 25 cents a shot while homemade "hooch" (this was originally an Alaskan word for home-brewed liquor, from the Chinook Jargon) went for as little as 40 cents a gallon! The latter bordered on toxic*, however. (A good reference for this is Boom and Bust in the Alaska Goldfields, by Steven Levi).
*-actually, it often crossed that border. I'm not kidding.