The move is not expected to be made official for a few days. Bowie has an off-day on Monday, meaning Bundy will likely start during Tuesday's doubleheader.
The No. 4 overall pick and top high school player selected in the 2011 MLB First-Year Player Draft, Bundy allowed four runs on seven hits and two walks in 5 1/3 innings in his start against Lynchburg on Wednesday.
In his first pro season, Bundy is 6-3 with a 1.92 ERA between Frederick and Class A Delmarva.
He began his career with Delmarva, allowing zero earned runs on only five hits and two walks with 40 strikeouts in 30 innings.
That earned him a promotion to Frederick, where he is 5-3 with a 2.98 ERA. In 54 1/3 innings, he has surrendered 48 hits and 17 walks with 63 strikeouts.
Bundy has thrown 84 1/3 innings this season, and the Orioles had planned to limit him to about 120.