I am not sure that there would have been time yet for a specific order to go out from Saruman... I think the crooks in Bree like Ferny were working for themselves for a buck or a favor, more than they were following any organized plan as yet from Saruman.
But there was one swarthy Bree-lander, who stood looking at them with a knowing and half-mocking expression that made them feel very uncomfortable. Presently he slipped out the door, followed by the squint-eyed southerner: the two had been whispering together a good deal during the evening. Harry the gatekeeper also went out just behind them.
Can't imagine that Tolkien included this without insinuating that others in the room (aside from Strider and the Hobbits) knews of the Ring. Your reply and others forced me to break out the book and get specific. Turns out only a Bree-lander made knowing expressions and that he was in in the company of just one of the southerners. Another fabulous scene in the LOTRs, but it raises some incidental questions for me :)