It depends what kind of alcohol you wanted to get.

Many wealthy people had huge stockpiles of the stuff from before the passage of Prohibition as it wasn't illegal to own if you had it prior to the law going into effect. Even the presidents through the time when Prohibition was active (Wilson and Harding) reportedly had fairly large stores of liquor that they moved to and kept at the White House for their own use. It wasn't illegal to drink alcohol according to the 18th Amendment which only banned the "manufacture, sale, or transportation [...], importation thereof into, or the exportation" of alcohol. If you already had it, you were free to drink it and a lot of people stocked up pretty heavily before the law passed.

The Volstead Act went into effect on October 28th of 1919 but it was initially passed by the Senate on September 5th of the same year so you had several weeks where people knew this was coming but it was still legal to buy alcohol.

Additionally you had a lot of people brewing or distilling their own "special" concoctions that they'd share with friends or neighbors they trusted and might pony you a bottle if you paid. There were companies that legitimately sold brewing materials during that time and the advertisements for the stuff were hilarious; they'd be selling "grape juice mix" but it would come with this big and oddly specific warning that under no circumstances were you to put the mix in with a cup of sugar and water and let it sit for two weeks in a cool dry place otherwise you'd be in violation of the Volstead Act.

You could also get medical permission to drink if you could convince (read: pay) a doctor to write you out a prescription. This worked roughly the same as medical marijuana does today, in every sense of that comparison. Religious organizations that used sacramental wines were also exempt and could own and use alcohol for these purposes and there was reportedly a lot of new converts to these religious orders during that time.

Further on you had the rise of speakeasies where you could get a drink but they were sometimes of questionable quality, the term "bathtub gin" (gin was the most popular hard liquor for bootleggers as it didn't require any aging so it could be cranked out rather quickly) comes from this time because many people did actually make it in their bathtubs or used water from their bath taps. It's posited that the cocktail came into widespread acceptance during this time because of this, the crappy taste of low-quality alcohol required something to make it drinkable so bartenders started adding in fruit juices or sugar so people wouldn't gag. I'm not 100% on this as I've never seen it seriously proposed as anything beyond hearsay so I wouldn't take it as gospel (though we do have records of several cocktails that originate from that time period).

As far as I'm aware (someone else feel free to chime in) we have no official estimates or information on how much an "average" bottle of firewater would have cost likely because there was no average. The alcohol varied widely in quality and you could get it a lot cheaper from a friendly neighbor than you could at a speakeasy.

In terms of how easy it was to get, I've seen figures that suggest that consumption actually went up during Prohibition though I don't know how valid that would be considering it was illegal. Judging from the number of loopholes and the level of illegal activity in general that was caught or later found out, it probably wasn't much harder to get a drink in 1920 than it was in 1918.