He was born in Southgate, Kentucky. His first game as a major league pitcher was on July 20, 1955. For the 1955 to 1963 seasons, he pitched for the Detroit Tigers, moving to the Philadelphia Phillies from 1964 through 1967, to the Pittsburgh Pirates from 1968 through the middle of the 1969 season (finishing the 1969 season on the Los Angeles Dodgers), and back to the Phillies, where he closed his career in 1970 and 1971. He wore uniform number 15 on the 1955 Tigers, switched to 14 in 1956, which was the number he wore for the Tigers, Phillies, and Pirates until he was traded to the Dodgers in 1969. For the Dodgers, he wore number 17, but returned to number 14 on being returned to the Phillies.
Bunning pitched his first no-hitter on July 20, 1958 for the Detroit Tigers against the Boston Red Sox. His second was a perfect game, which came against the New York Mets on June 21, 1964, the same day that the civil rights workers Andrew Goodman, James Chaney, and Michael Schwerner were murdered in Neshoba County, Mississippi. He is one of only five players to throw a no-hitter in different leagues.
He was first elected to political office in 1977, where he served on the city council of Fort Thomas, Kentucky until 1979. He then went into the Kentucky State Senate, serving from 1979 to 1983. He was nominated for Governor of Kentucky as a Republican candidate in 1983, but was defeated; four years later he became a Representative from Kentucky, serving until 1998, when the voters elected him to the United States Senate.