Dunbar accepted an athletic scholarship to attend the University of Florida, where he played for coach Urban Meyer and coach Will Muschamp's Florida Gators football team from 2010 to 2014. Dunbar was a wide receiver for the Gators over five seasons. In his freshman season, he played in one game in 2010 against Miami (OH) on opening day and ultimately redshirted.
After going unselected in the 2015 NFL Draft, Dunbar was considered one of the top undrafted free agent wide receivers available. He signed with the Washington Redskins on May 11, 2015. Due to camp injuries to cornerbacks on the roster, the team moved him to cornerback. On September 5, he was waived during final roster cuts before the start of the regular season, but signed to the team's practice squad the next day. On September 29, 2015, he was promoted to the active roster. On November 29, 2015, he had his first career interception after he intercepted Eli Manning of the New York Giants in the end zone.
Dunbar had a large impact in the Week 3 win over the New York Giants. He recorded his second career interception, picking off Eli Manning in the end zone, and recorded his first career catch on a 31-yard pass from punter, Tress Way, on a fake punt play.