On December 8, 2016, Bemboom was selected by the Colorado Rockies in the minor league portion of the Rule 5 draft.[6] He played for the Triple–A Albuquerque Isotopes in 2017, slashing .278/.390/.459 with four home runs and 20 RBI.[5]
Bemboom returned to Triple–A Albuquerque in 2018, playing in 70 games and hitting .232/.339/.351 with five home runs and 29 RBI. He elected free agency following the season on November 2, 2018.[7]
Tampa Bay Rays
On November 26, 2018, Bemboom signed a minor league contract with the Tampa Bay Rays.[8] He began the 2019 season playing for the High–A Charlotte Stone Crabs and the Triple–A Durham Bulls.[5] On May 10, 2019, Bemboom was selected to the 40-man roster and promoted to the major leagues for the first time.[9] He made his major league debut on May 12 versus the New York Yankees.[10] Bemboom tecorded his first career hit on May 14, an RBI double against the Miami Marlins. He later exited the game with a knee injury.[11] He was placed on the injured list on May 16.[12] On July 15, he was reinstated from the injured list and subsequently designated for assignment.[13]
Los Angeles Angels (second stint)
On July 15, 2019, Bemboom was traded to the Los Angeles Angels in exchange for cash considerations.[14] On August 24, 2020, Bemboom made his first career pitching appearance against the Houston Astros, pitching a scoreless inning after getting Carlos Correa, Taylor Jones and Michael Brantley to fly out following the walk of Kyle Tucker. In 2020, Bemboom batted .208/.328/.417 with 3 home runs and led all Angels catchers with a 41% caught stealing rate.[15] On August 7, 2021, Bemboom was designated for assignment by the Angels.[16]
Los Angeles Dodgers
On August 9, 2021, the Los Angeles Dodgers claimed Bemboom off waivers from the Angels.[17] On August 14, Bemboom was outrighted off of the 40-man roster without having appeared in a game for the Dodgers.[18] He played in 25 games for the Triple-A Oklahoma City Dodgers, with a .189 batting average.[5] Bemboom became a free agent following the season.
Baltimore Orioles
On December 16, 2021, Bemboom signed a minor league contract with the Baltimore Orioles organization.[19] He made the Orioles' Opening Day roster for the 2022 season.[20] Playing in 22 games for Baltimore, Bemboom hit just .115/.207/.212 with one home run and one RBI. He was designated for assignment on May 21, 2022. He cleared waivers and was sent outright to Triple-A Norfolk Tides on May 27. Spending the rest of the season in Norfolk, Bemboom appeared in 34 contests, batting .228/.292/.350 with 3 home runs and 15 RBI.
Following the 2022 season on October 6, the Orioles added Bemboom to the 40-man roster to prevent him from reaching minor–league free agency.[21] However, on November 4, Bemboom was removed from the roster and sent outright to Triple–A Norfolk.[22]
On March 30, 2023, Bemboom had his contract selected after making the Opening Day roster. James McCann had suffered an injury and a backup catcher was needed, necessitating his promotion.[23] After going 0–for–2 in just 2 games, he was designated for assignment on April 13.[24] He cleared waivers and was sent outright to Triple–A Norfolk the same day.[25] On June 20, Bemboom was selected back to the major league roster to replace José Godoy as the backup to Adley Rutschman.[26] He went 2–for–9 in 4 more games, and was again designated for assignment on July 5, following the promotion of Colton Cowser.[27][28] He again cleared waivers and was sent outright to Norfolk on July 12.[29] On October 13, Bemboom elected free agency.
Detroit Tigers
On December 8, 2023, Bemboom signed a minor league contract with the Detroit Tigers.[30] On November 6, he elected free agency.[31]