Bibby's best year in the majors was in , when he posted a 19–6 record and a league-best .760 win-loss percentage. He also made his only appearance in an All-Star Game that season at Dodger Stadium on July 8. He entered the game in relief of Jerry Reuss and pitched a scoreless seventh inning. 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.