Bradford was optioned to Triple-A Round Rock on Tuesday.
Bradford pitched well in spot duty his past two outings with three earned runs allowed across eight innings, and he'll head down to the minors with Texas' trade acquisitions joining the active roster. The 25-year-old has a 4.50 ERA, 1.23 WHIP and 37:11 K:BB across 40 innings this season, and it's likely only a matter of time before he rejoins the big-league bullpen.