a barmance is like a bromance but instead of your guy friend, it's a relationship between the local watering hole's bar staff and you, their loyal customer. it might mean just free drinks but who knows what it might lead to...
"hey, did you see bob?"
"yeah, he's talking to jane again...that's such a barmance"
"why doesn't he just ask her out?"
"good question. he tips her like 50% every night"