Bullard attended Crest Senior High School in Shelby, North Carolina.

[4][5] Bullard returned to Florida his senior season rather than enter the 2015 NFL draft.

[13] On October 9, Bullard recorded his first sack of his career, taking down Indianapolis Colts' Andrew Luck.

[14] He finished his rookie season with one start in fourteen games, recording eighteen tackles and a sack.

Bullard recorded his first career pass break-up on September 28, 2017, as well as a tackle against the Green Bay Packers.

On October 29, he logged his first forced fumble against the New Orleans Saints, stripping running back Mark Ingram II[15] In a blowout loss to the Philadelphia Eagles, Bullard got his first and only sack of the 2017 season, bringing down quarterback Carson Wentz on November 26.

[22] On October 7, 2020, Bullard was signed to the active roster of the Seattle Seahawks off the Cardinals' practice squad.