Stay on your side of the bar
There's nothing that pisses off a bartender more than a trespassing customer. I don't care if you're trying to shake a hand, clean up a spill, or catch a mouse, violating that sacred line between server and served will definitely gain you a permanent spot on any bar's shit list. If help is needed back there, you'll be asked.
Entitlement is perhaps the worst quality in a human being, and that counts double for anyone trying to achieve regular status. Acting like you deserve perks like extra shots, buybacks, or music and TV requests is a big turnoff, so remember to be polite and gracious at every turn. The same goes for assuming your bartender-customer relationship extends beyond the confines of the bar. Always take cues from the staff -- if they want to hang out off shift, rest assured they'll make it known. Until then, cozy up to that barstool, mind your P's and Q's, and keep happily nursing that beer.