Public relations? Jamie's mouth pulls off to the side in such a way to suggest he doesn't believe that for one moment, but all he says is "Ah. Well, enjoy your ale."

He turns away, leaving Jayne to his own devices. Without his own ale to occupy him, however, there's not too much to do, and he keeps glancing over towards the entrance to the tavern. "Och," he mutters to himself after a few minutes. "Kaylee, where are ye?"

It doesn't appear that he's realized that he's said it loudly enough that Jayne could pick up on the words - especially since he hasn't bothered to move from his seat next to the man.