Bummer was optioned to Triple-A Charlotte on Wednesday, Daryl Van Schouwen of the Chicago Sun-Times reports.
The White Sox are expected to announce a corresponding roster move prior to Thursday's series finale against the Twins. Bummer owns a solid 3.26 ERA and 21:6 K:BB across 19.1 innings this season, so he'll likely be back with the big club when a fresh reliever is needed.