The Boston Red Sox signed Bazardo as an international free agent in July 2014 for $8,000.

He pitched solely as a starter in 2018, starting with the Low-A Lowell Spinners and being promoted to the Single-A Greenville Drive in early August.

In 2019, he returned to the bullpen and again played at two levels, beginning the year with the High-A Salem Red Sox and advancing to the Double-A Portland Sea Dogs in mid-June.

[3] Through 2019, Bazardo compiled a record of 23–19 in 100 games, including 31 starts, with 10 saves in five minor-league seasons.

[13] He did not pitch for the Red Sox in his final stint with the team in 2021 and was optioned back to Worcester on October 3, after the end of the regular season.

With Worcester, he appeared in 11 games and registered three saves while pitching to an 8.74 ERA and striking out 12 batters in 11+1⁄3 innings.

[17] On October 5, Bazardo earned his first career win after tossing a scoreless fifth inning in a 6–3 victory over the Tampa Bay Rays.

[27] He joined the Tacoma Rainiers after the trade but was on the Mariners roster two times, from August 17 to 22 then again from September 10 until the end of the season.