Bradley began his college career in 2009 after attending Prince George High School in Prince George, Virginia. Prior to attending college, he had been named to the 2008 Virginia AAA All-State team and was listed as the 40th-best Virginia-based baseball prospect for the 2008 Major League Baseball draft by Baseball America.

With the University of South Carolina in 2009, Bradley hit .349 and scored 69 runs in 63 games. Posting a slugging percentage of .537, he hit 11 home runs while walking 34 times and striking out 31 times. He spent the summer in the Cape Cod League with the Hyannis Mets.

In 2010 he batted .368 and 13 home runs, driving in 60 runs while scoring 56 times in 67 games. Then, he went 10-for-29 at the plate in the 2010 College World Series, earning CWS Most Outstanding Player honors.

Bradley was selected 40th overall by the Boston Red Sox in the supplemental first round of the 2011 Major League Baseball Draft. Bradley made his professional debut on August 23, 2011 with the Class-A Short Season Lowell Spinners, hitting .250 in 10 games split between the Spinners and Single-A Greenville Drive. Bradley was named Minor League Defensive Player of the Year by the Red Sox organization for the 2012 season. He hit .315 with 55 extra-base hits, 87 walks, and 63 RBIs in 128 games.

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