As the previous poster said, a $1 per drink is good if you're going back and fourth to the bar.
However, if you're sitting there awhile at the bar with the same bartender and running a tab, it is acceptable to tip less when you settle up.
Example: If I had 6 drinks at $5 a pint, thats $30. For that I would give a $5 instead of a $6.
Since the amount in question is so minor, its better to stick with $1 a drink. Easier.
However, I would point out that if you get a buy-back then you should tip more. A basic guide is if the bartender 'buys' you a $5 drink then you should be giving $2 towards the final tip.
Thats just a simple guide for a simple use-case. Use your discretions. I don't tip if the bartender is rude or gives me a sloppily poured drink (I say that as a former bartender/bar-back/bar-manager).