The left-hander threw 35 pitches in a side session Saturday afternoon, and said afterward he didn't feel any discomfort. He's been bothered by both his left knee and left lat.
"I'll have to see how it reacts," Bedard said when asked where he goes from here. "The next day is always the big key."
As for Monday's twin bill with the Orioles at Fenway, John Lackey is set as the nightcap's starter, but the Sox haven't made any commitments for the early game.
"I don't know. We'll see," manager Terry Francona said. "We got some moving parts obviously, want to see how [Bedard] comes through this [throwing session], and then we want to gauge where we think he is, and then we can make some decisions. We'll have something for you guys pretty soon. We got some either-ors, obviously."
Dealing with a plethora of other injuries, the Red Sox saw little improvement from Kevin Youkilis (hip) on Saturday, while Jed Lowrie (left shoulder) was faring "much better" Francona said.