Bummer (1-1) was credited with the win Monday against the Astros, giving up one hit in a scoreless two-thirds of an inning.
Bummer (0-1) got charged with a blown save and took the loss Sunday against the Phillies, giving up two runs on four hits while striking out one in the seventh inning.
Bummer gave up a run on two hits while striking out two in an inning of relief during Thursday's Grapefruit League game against the Rays.
Bummer was traded from the White Sox to Atlanta on Thursday in exchange for Michael Soroka (forearm), Jared Shuster, Nicky Lopez, Braden Shewmake and Riley Gowens.
Bummer has recorded three holds in his last five appearances for the White Sox.
Bummer (lat) is scheduled to appear in Friday's Cactus League game against the Athletics, Scott Merkin of MLB.com reports.
Bummer (lat) threw a bullpen session Thursday, James Fegan of The Athletic reports.
White Sox manager Pedro Grifol said Wednesday that Bummer (shoulder/lat) is on track to be ready for Opening Day, Daryl Van Schouwen of the Chicago Sun-Times reports.
Bummer picked up the save Saturday against the Tigers, allowing one run on one hit while striking out one and walking none over one inning.
Bummer (shoulder) was transferred to the 60-day injured list Friday.