Hmmm, how to cost Bartender...
I'll be honest, I like where Town Drunk and Bartender are at right now. Town Drunk is a card I would never buy without Bartender being around. Now a call Town Drunk, play Bartender, play Town Drunk and then call Town Drunk turn? That's a reason to buy Town Drunk, I think. Yes, you're getting $4 but you're also spending $4 for the two cards, and you need to expend some actions to do it...
The question for Bartender costs then is, how powerful is it with other Reserve cards?
The short answer is, not *that* powerful, but:
With Guide and Ratcatcher, if you play the Reserve card, you can get an additional +1 Card and +1 Action, making Bartender in essence a Laboratory that moved a Guide or Ratcatcher onto your Tavern mat. That's $5 + probably less than $1 worth of tempo. Or maybe $1 worth of tempo. That's POWER, you say, but bear in mind that you also needed a $2 or $3 second card and a bit of setup (having the Guide or Ratcatcher on your Tavern Mat) in order to gain the bonus. So at most this combo would imply that Bartender should cost $3. But it's a combo, so not necessarily.
With Coin of the Realm, Bartender essentially gives you +1 Card, +1 Action, +$1. For about $4 worth of cards and some set up cost. I'd price that as $4 or $5, as it's a Peddler variant where the drawback is "you must have a Coin of the Realm in play before playing this."
With Teacher, Bartender is "+1 Card, skip having to shuffle before you get a Teacher ready for next turn". This *is* powerful as it basically lets Bartender count as a copy of Teacher, tempo-wise. But is that tempo worth ~$8, with the setup requirement -- working to get Bartender, working to upgrade up to Teacher, getting a Teacher in play with a Bartender at the ready? You had to have a Teacher in play, and you have to wait til next turn to play Teacher again. Hmmm.
Duplicate is a lot like Teacher, but then you probably had to call Duplicate early, during your Action phase. How good of a card are you getting with Duplicate, then? I feel like Duplicate's power level will be lessened if you use it with Bartender, so it likely balances out. Weaker Duplicate, two turns in a row, for $6 over two cards? Probably fine.
Transmogrify and Royal Carriage basically make Bartender "Cantrip, get a Transmogrify or Royal Carriage ready again." Of course, Royal Carriage could then be used again this turn on whatever you use its Action on, which is powerful but not outside how Royal Carriage already worked. The most powerful use of this would be if you have multiple Bartenders and Royal Carriages in your hand with Town Drunks? This sounds more fun than broken, though. Again.. cost? Probably not more than the cost of buying a Royal Carriage and a Bartender ($6).
Finally, for the sake of completeness, Distant Lands and Wine Merchant don't interact with Bartender at all. Which is probably a good thing.
In conclusion, Bartender is probably fine at $2. If you test it and find it is too powerful, consider bumping it up to $3 to deal with the Teach and Royal Carriage and Guide/Ratcatcher power spikes.