Verisimilitude: The quality of appearing to be true or real.
Deadwood does a good job, but verisimilitude is often achieved by catering to what people have been conditioned to expect, rather than to true accuracy.
The Deadwood TV series begins in 1876 and moves forward from there. At that time, most whiskey would have still come in by the barrel, but bottled whiskey would not have been unknown. Especially in a gold-mining boom town like Deadwood, bottled whiskey is exactly the kind of luxury good that would have been available for a price.
However, the show tends to give us what appears to be a bottled product, with a paper label on it, in almost every instance, which probably is not accurate. Ceramic jugs probably would have been more common in reality than they are on the show. A character like Jane, for example, who is drinking the cheapest thing she can find, probably should be shown drinking from a jug, not a glass bottle.
The mention of Basil Hayden is either a product placement or a homage by the film maker. Likewise anything that looks like Bulliet, which is based on old apothecary bottles, not old whiskey bottles.
The problem is not so much that they are showing bottles but that the bottles appear to have paper labels on them. Whiskey was served from bottles but they were "house" bottles that were used like decanters. The Bella Union might have had fancy crystal ones while the Gem would have had what appeared to be plain bottles, but they would not have had any kind of label on them.