In his start Friday night against the Tigers at Safeco Field, Bedard worked five innings.
"We took him out of the game because of the game situation, but he told the trainer that his [shoulder] was tight. He said he felt better [on Saturday]."
Riggleman said shutting down Bedard until after the All-Star break was an option, but, "I don't want to think that way."
"Reports from the trainer and doctor indicate they think it will be all right. I guess that would be a possibility if he's not [feeling better], but we're anticipating that he will pitch later this week."
Right-hander Miguel Batista, who tossed two impressive innings of relief in Saturday night's victory over the Tigers, is tentatively slated to start Wednesday night's game in Oakland, depending on whether or not he's used in relief before then.
If Batista isn't available, right-hander R.A. Dickey would get the Wednesday start.
Meanwhile, injured right-hander Felix Hernandez is getting close to rejoining the rotation. He had a bullpen session prior to Sunday's series finale against the Tigers and will have another, lighter, session on Tuesday in Oakland.
"If everything goes well, he would pitch either Thursday [in Oakland] or Friday [in Kansas City]," Riggleman said.
Hernandez has been sidelined since spraining his left ankle in a home-plate collision on June 23 against the Mets in New York.
Closer J.J. Putz, who is eligible to come off the 15-day disabled list, might begin a rehab assignment during the All-Star break and rejoin the staff later in the month.
"I haven't received a schedule from anybody that nails it down, but it seems to me that if everything goes good here the next week, maybe sometime during the break he could get a rehab appearance and maybe one more after that. He could be back about a week after the break."