Bailey suffered the injury during a spring training appearance on March 14 and the A's feared he'd suffered an elbow injury, going so far as to set him up with a visit with Dr. James Andrews.
"It's safe to say I'll miss a little time," Bailey said after throwing again for the first time Sunday. "But better now than a month or two or three down the road."
"I could use either one," Geren said. "Fuentes has the most experience. I feel comfortable with him. I also know Grant can do it if it's better to use someone else in a different inning."
Bailey, a two-time All-Star and the 2009 AL rookie of the year, had 25 saves last year for Oakland and a 1.47 ERA.