During a 12-year baseball career, he pitched from 1972 to 1984 with the St. Louis Cardinals, Texas Rangers, Cleveland Indians, and Pittsburgh Pirates, with whom he was a member of its 1979 World Series champions.

[3][5] After appearing in thirteen games and posting a 2–3 record with an 11.25 ERA with the Marion Mets in 1965,[6] he spent the next two years on active duty with the United States Army as a truck driver in Vietnam.

[7][8] On his return to baseball, Bibby moved up the organization's minor league system, first with the Raleigh-Durham Mets in 1968 before splitting time with the Memphis Blues and Tidewater Tides in 1969.

[6] His progress was interrupted again in 1970 when a back injury which required a spinal fusion of the first and second vertebrae sidelined him for the entire season and put his career in doubt.

[9] Bibby never got to pitch for New York because he was part of an eight-player transaction on October 18, 1971, when he, Art Shamsky, Rich Folkers and Charlie Hudson were sent to St. Louis for Chuck Taylor, Chip Coulter and two players who would help the Mets capture the National League pennant in 1973, Jim Beauchamp and Harry Parker.

[10] Bibby earned a promotion to the Cardinals late in 1972 as the Tulsa Oilers' top hurler at 13–9, with a 3.09 ERA, 13 complete games and 208 strikeouts.

[11] He made his major-league debut at age 27 as the starter in the second game of a Labor Day doubleheader at Busch Memorial Stadium on September 4.

"[14] On July 30, Bibby no-hit the defending and eventual repeat World Champion Oakland Athletics 6–0 at the Oakland–Alameda County Coliseum, the first no-hitter in the franchise's history.

[18] When the Billy Martin-managed Rangers became the surprise team of 1974 by going 84–76 and vaulting into second place in the American League Western Division, Bibby (19–19) and the newly acquired Ferguson Jenkins (25–12) each made a club-record 41 starts to anchor the pitching staff.

[4] More importantly, with the help of pitching coach Harvey Haddix, he worked on improving his delivery to home plate and also added the curveball, slider and changeup to his repertoire.

[25] When the Pirates clinched the series with a 4–1 win in Game 7 at Memorial Stadium, he lasted four innings, with his only mistake being Rich Dauer's home run to lead off the Orioles' third.

After Robin Yount flied out to right field, Bibby surrendered a single to center to Willie Randolph, who was retired when Cecil Cooper grounded to the shortstop for a double play.

Bibby also excelled at the plate that night by hitting a pair of doubles (to center off Phil Niekro in the fifth, to left off Rick Mahler in the sixth), driving in a run and scoring another.

After replacing Dave Tobik to start the ninth inning, Bibby allowed a single to Joel Skinner, a double to Rudy Law and an intentional walk to Jerry Hairston, Sr. to load the bases with one out.