Bonser, who missed all of last season with shoulder surgery, has been battling a sore right groin. He pitched three innings in a simulated game Monday and is expected to throw in a minor league game Saturday in Florida when the big club heads north to play in Washington.
Expected to provide depth in the system in the event the Sox need a fill-in starter, Bonser went 0-2 with an 11.57 ERA in four Grapefruit League appearances.
Lowrie, who battled wrist issues all of last season, has been absent from the club since early March with mononucleosis. Manager Terry Francona said this week that Lowrie has barely been able to resume any activities, much less anything related to baseball.
Due to Lowrie's illness, the club recently bolstered its infield depth with the acquisition of Kevin Frandsen from San Francisco. Frandsen was optioned to Triple-A Pawtucket. Infielder Tug Hulett remains in the big league camp.