[6] After the season, he played in the Cape Cod Baseball League for the Yarmouth–Dennis Red Sox, earning Pitcher of the Year honors after going 4–1 with a 1.65 ERA in 32+2⁄3 innings.

[11][12][13] He made his professional debut with the Idaho Falls Chukars where he was named a Pioneer League All-Star.

[19] Bubic made his major league debut on July 31, 2020, against the Chicago White Sox, pitching four innings while allowing three earned runs and striking out three.

[20] With the 2020 Kansas City Royals, Bubic made ten starts, compiling a 1–6 record with 4.32 ERA and 49 strikeouts over fifty innings pitched.

On April 21, 2023, it was announced that Bubic would undergo Tommy John surgery, prematurely ending his season.