McBride played at the College of William & Mary from 2011 to 2014. As a freshman, he played in all 11 games and had 14 receptions for 146 yards. He was the first freshman wide receiver to play for William & Mary since 2005. As a sophomore, McBride started all 11 games and led the team with 55 receptions for 897 yards and 10 touchdowns. As a junior, he started 11 of 12 games and again led the team with 63 receptions for 801 yards and five touchdowns. He was also the kick returner and led the team with 1,533 total all-purpose yards. As a senior, he had 64 receptions for 809 yards and four touchdowns. Against Villanova, he set the school record for most all-purpose yards in a game with 359.
McBride was drafted by the Tennessee Titans in the seventh round, 245th overall, in the 2015 NFL Draft. On September 5, 2015, he was waived and was signed to the practice squad the next day. On November 17, 2015, McBride was elevated to the active roster.
McBride was waived by the Titans on September 5, 2016. The next day, he was signed to the Titans' practice squad. He was promoted to the active roster on November 1, 2016.
On September 2, 2017, McBride was waived by the Titans.
On September 3, 2017, McBride was claimed off waivers by the Chicago Bears. He was waived on September 23, 2017 and was re-signed to the practice squad. He was promoted back to the active roster on October 2, 2017. He was waived on November 28, 2017.
New York Jets
On December 1, 2017, McBride was signed to the New York Jets' practice squad. He signed a reserve/future contract with the Jets on January 1, 2018.
On September 1, 2018, McBride was waived by the Jets.
On January 2, 2019, McBride signed a reserve/future contract with the Washington Redskins, with him later being waived on April 30, 2019.