Bennett represented the United States at the 1960 and 1964 Summer Olympics. At the 1960 Rome games, he received a bronze medal for his third-place result in the men's 100-meter backstroke, finishing in 1:02.3 – a fraction of a second behind Australian David Theile (1:01.9) and fellow American Frank McKinney (1:02.1). He also swam for the gold medal-winning U.S. team in the heats of the 4×100-meter medley relay, setting a new world record of 4:08.2 in the process.[2] He did not receive a medal, however, because he did not swim in the event final, and was not medal-eligible under the 1964 Olympic swimming rules.
Four years later at the 1964 Tokyo games, he won a second bronze medal in the men's 200-meter backstroke (2:13.1).[3] He again swam for the first-place U.S. team in the preliminary heats of the 4×100-meter medley relay,[2] but was again ineligible to receive a medal.
Bennett set a new world record of 1.01.3 in the 100-meter backstroke on August 19, 1961; the record survived for twelve months until broken by American Tom Stock.