During his minor league playing career, Bright was known for his versatility in the field, his batting ability, and his frequent changes of address. He played every infield position, caught and played the outfield. In a 12-year stretch, 1947 through 1958, he played for 14 different minor league teams and at least four different MLB organizations. At the plate, he led the Class CWest Texas–New Mexico League in batting average in 1950 with a.413 mark. Two years later, as the 22-year-old playing manager of the Janesville Cubs of the Class D Wisconsin State League, Bright led the league in runs batted in with 101 — although Janesville finished seventh in the eight-team WSL. Bright's best minor league season came when he was a 30-year-old veteran playing for the 1960 Salt Lake City Bees in the Pacific Coast League. He slugged 27 home runs, led the PCL with 119 RBI and batted.313. Bright was a fixture in the Pacific Coast League of the 1950s, having played three and a half seasons for the Sacramento Solons. He became a resident of Sacramento, California, and later managed the Solons in 1975.
Bright's first major league trials came with the Pittsburgh Pirates, where he played in parts of the 1958 and 1960 seasons, and spent all of 1959 on the Pirates roster, appearing in 40 games in a utility role. On December 16, 1960, he was traded to the American League's new expansion franchise, the Washington Senators, where he played two full seasons and enjoyed his most sustained success. In 1962, he appeared in 113 games, mostly at first base, swatted 17 homers, knocked in 67 RBI and batted.273. But at season's end, the Senators swapped the 33-year-old Bright to the Cincinnati Reds for a young first baseman, Rogelio Álvarez. Bright batted only once for the 1963 Reds before his contract was sold on April 21 to the defending world championNew York Yankees, who were seeking a right-handed hitter off their bench. He stuck with the club all season long, batting.236 with seven homers in 157 at-bats as the Yanks copped another AL pennant.
Then, in Game 1 of the 1963 World Series, Bright made history when he was sent up as a ninth-inning pinch hitter against Sandy Koufax of the Los Angeles Dodgers. Bright struck out, enabling Koufax to set a new mark for strikeoutsin a World Series game. Said Bright: "It's a hell of a thing. I wait 17 years to get into a World Series. Then I finally get up there, and 69,000 people are yelling — yelling for me to strike out." To compound matters, the game was played in Bright's home ballpark, Yankee Stadium. Bright struck out again in his only other World Series at bat and by mid-May 1964 he had returned to the minors with the Triple-ARichmond Virginians. His MLB career ended in 1965, as a pinch hitter for the Chicago Cubs. All told, Bright appeared in 309 MLB games over all or parts of eight seasons, batting.255 with 214 hits, 31 doubles, four triples, 32 homers and 126 RBI.