It all depends on the use of the sink. Typical counter height ranges from ~ 30 inches to 36 inches. In bathrooms it is typically lower - 30 - 32 inches, but 36 inches is standard for kitchens in the US (dishwashers and slide-in ranges are sized based on a 36 inch high counter). A sink can even be a little higher, though above 36 inches a sink can be harder to use for shorter people. A lot also depends on the use - washing hands is different from washing big pots & pans.
Figuring on a bar sink with a depth of 10" (from a quick search, but I think that is typical), and adding a few inches for sink drain, coupling to trap, etc., my guess is your counter height (top of sink) should be somewhere in the 42" - 46" range. A quick search shows typical wet bar height at 42". That is really for the part between the bartender and the customers. The sink area behind the bar can be lower, but at least that gives a basis for a 42" height. A shallower sink (~ 8" instead of 10") would definitely help too.
If you are getting a plumber to do the work, I suggest you have them review the design before you purchase cabinets, counters & sink. If you are doing the plumbing yourself then come back with more specifics once you have a planned design and one of the experts (I'm not a plumbing expert) can review in more detail.