The Cleveland Guardians selected Bibee in the fifth round of the 2021 MLB Draft.[5] He made his professional debut in 2022 with the Lake County Captains.[6] Splitting the year between Lake County and the Double-A Akron RubberDucks, Bibee worked to a combined 8-2 record and 2.17 ERA with 167 strikeouts in 1322⁄3 innings pitched across 25 starts. He began the 2023 season with the Triple-A Columbus Clippers, posting a 2-0 record and 1.76 ERA with 19 strikeouts in 3 starts.[7]
On April 26, 2023, Bibee was promoted to the major leagues for the first time.[8] He made his major league debut the same day as the starting pitcher against the Colorado Rockies. In his debut, Bibee became the first Cleveland pitcher in the live-ball era (1920-present) to record at least five consecutive strikeouts in a Major League debut. He ended the game with a final line of 52⁄3 innings pitched with 8 strikeouts and 1 earned run while recording his first career win.[9] In 25 starts for Cleveland, Bibee posted a 10–4 record and 2.98 ERA with 141 strikeouts in 142.0 innings of work.[10] On September 24, it was announced that Bibee would miss the remainder of the year with right hip inflammation, and was subsequently placed on the 60–day injured list.[11]