During his minor league playing career, Bright was known for his versatility in the field, his batting ability, and (during the era before free agency in baseball) his frequent changes of address.

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.

Bright batted only once for the 1963 Reds before his contract was sold on April 21 to the defending world champion New York Yankees, who were seeking a right-handed hitter off their bench.

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.

He later managed in the Kansas City Royals, Oakland Athletics, Milwaukee Brewers and Atlanta Braves organizations, and scouted for the Montreal Expos.