Morrow won the 1955 AAU 100-yard title. His most successful season was in 1956, when he was chosen by Sports Illustrated as "Sportsman of the Year". Morrow won the sprint double in the national college championships and defended his AAU title. Morrow then went to the 1956 Summer Olympics in Melbourne, where he won three gold medals and was the leader of the American sprint team.
In all, Morrow won three gold medals. First, he was victorious in the 100-meter dash. He then led an American sweep of the medals in the 200-meter dash, while equaling the World Record at that distance. He won his third gold by anchoring the 4×100-meter relay team to a World Record time. The three performances are encapsulated in Video on YouTube.
Morrow's success on a national level continued after the Olympics, but he retired in 1958 to become a farmer and a woodworker. He made a short comeback before the 1960 Olympics but failed to qualify for the US Olympic team.
In October 2006, San Benito High School named its new 11,000 seat sporting facility Bobby Morrow Stadium. Mr. Morrow was on hand to help dedicate the new facility.