You are incorrect!
The Bartender, Mr. Conway, is not the killer
The unknown individual he was texting and who he met on his smoke break was his bookie. Mr. Conway is deeply in debt with this person and is afraid of what will happen if he doesn't pay up. He fears that if he is seen talking to the police his bookie will think he is turning him in. Sure, Mr. Conway did not like Jill and really couldn't afford to lose his job because of her, but his gambling debt and the problems with the bookie are all that's on his mind.