Growing up, Bazardo played in Venezuelan youth leagues, where one of his competitors was future teammate (on two different MLB clubs) Miguel Cabrera.

His first season in the organization was in 2001, when he played for the now-defunct VSL Marlins in the Venezuelan Summer League, going 7–2 with a 2.43 earned run average (ERA).

[5] A further sign of the Marlins confidence came in 2005, when Bazardo was invited to spring training, although he did not make the cut and was optioned to the double-A Carolina Mudcats.

[7] Bazardo stayed with the Mudcats through the end of July, going 8–7 with a 3.99 ERA, when he was traded with Mike Flannery to the Seattle Mariners for Ron Villone.

The Mariners added Bazardo to their 40-man roster, but designated him for assignment after acquiring veteran pitcher Jeff Weaver.

Assigned to their AAA affiliate, the Round Rock Express, Bazardo was named a Pacific Coast League midseason All-Star.

On August 8, the Astros purchased Bazardo's contract, and he pitched in ten games for Houston through the end of the season, making six starts.

In 2011, Bazardo pitched for the Camden Riversharks of the Atlantic League of Professional Baseball, registering a 7.50 ERA across 4 games for the club.

After not playing affiliated ball in 2012, Bazardo joined the Telemarket Rimini of the Italian Baseball League for the 2013 season, pitching to a 4–0 record and 2.59 ERA across 7 appearances.