I don't know where they got their data, but my guess is that the discrepancy has something to do with the fact that Virginia doesn't actually have "bars" as a legal category of establishment. Instead, most bars are classified by ABC as "restaurants" and have to serve at least a certain amount of food in order to be able to sell alcohol.
So I've used ABC's license search to reproduce this map at a local level - this time including breweries, clubs, and restaurants that serve alcohol (though I didn't count hotels). This might be casting the net a little too wide for the term "bar," but it's more accurate than not counting restaurants with ABC licenses - most of which have a bar of some kind or function as one after hours. I came up with a statewide number of 1,048 people per establishment. Unsurprisingly, college towns and tourism destinations lead the way. You can make some loose correlations with income or with median age - but both have a lot of outliers.
Top 20/Bottom 20: