Bourque returned to action in 2016 with the Single–A Hagerstown Suns. In 17 games (13 starts), he logged a 5–6 record and 5.03 ERA with 55 strikeouts in 68 innings of work.[4] Bourque spent the 2017 season back with Hagerstown, making 23 appearances (20 starts) and registering a 5–7 record and 5.07 ERA with 90 strikeouts in 113+2⁄3 innings pitched.[5]
Prior to the 2018 season, the Nationals converted him from a starter into a relief pitcher. Bourque turned in a 1.70 ERA between the High-A Potomac Nationals and Double-A Harrisburg Senators, working exclusively in relief, and rocketed up the prospect charts to be ranked as the Nationals' 17th-best prospect by MLB.com midway through the 2018 season. On November 19, 2018, the Nationals added Bourque to their 40-man roster to protect him from the Rule 5 draft.[6][7]
After Bourque pitched to a 1.33 ERA through 14 games with Double-A Harrisburg, the Nationals called him up on May 25, 2019, to replace Joe Ross in the bullpen.[8] He made his major league debut the following game, pitching in the ninth inning against the Miami Marlins. On May 29,, Bourque was optioned to the Triple-A Fresno Grizzlies and spent the rest of the season there,[9] going 4–1 with a 5.56 ERA over 43.2 innings.[10]
In 2020, Bourque made six major league appearances for Washington, recording a 6.75 ERA with only one strikeout in four innings of work.[11] He missed the latter part of the season due to an elbow strain, and was removed from the 40-man roster and sent outright to Triple–A on October 13, 2020.[12] Bourque became a free agent on November 2.[13]
Chicago Cubs
On December 18, 2020, Bourque signed a minor league contract with the Chicago Cubs organization.[14] He missed the entire 2021 season due to injury, and made only 7 appearances for the Triple-A Iowa Cubs in 2022, logging a 3.24 ERA with 16 strikeouts in 8+1⁄3 innings pitched.[15] Bourque elected free agency following the season on November 10, 2022.[16]
San Diego Padres
On May 17, 2023, Bourque signed a minor league contract with the San Diego Padres organization.[17] In 11 games for the Double–A San Antonio Missions, he recorded a 3.46 ERA with 18 strikeouts in 13.0 innings of work. On July 25, Bourque was released by San Diego.[18]