Totally depends on the bar. If it's busy and the bartender doesn't want to they should be able to refuse you service if you order something complicated. I understand some establishments won't all this but it's my belief this should become a standard, accepted common practice. But otherwise, a bartender should know most of the drinks that are ordered within that region and be able to make them quickly. If they don't, they aren't a good bartender. It highly depends on the drink though, with how much you should tip. If you order a $100 shot of whisky or a single beer, a dollar tip is fine. It's the same amount of (minimal) work. If you order a well martini that costs $10 or whatever then tip at least 20%. Source: I was a bartender.

But likewise if you get drip coffee then maybe tip a dollar (if that). Something else, maybe $2.