The club was established in 1904. They made their first final appearance in the 1913 season, when they defeated S.C.U.F. 31–8 at the Stade Yves-du-Manoir. The national domestic championship was replaced by the Coupe de l'Espérance during World War I. This competition was played for four seasons, with Aviron Bayonnais contesting the last final, which they lost to Stadoceste Tarbais 4–3.
With the French championship resumed, the club made their next championship game in the 1922 season, when they met Toulouse. Bayonne lost the final 6–0. The two teams would contest the championship final once more the next season, which Toulouse won again, 3–0.
Aviron Bayonnais enjoyed success during the mid-1930s, beating Biarritz 13–8 in Toulouse to win their second championship, their first since 1913. They also won the Challenge Yves du Manoir in 1936, defeating Perpignan in the final. The club saw similar results during the mid-1940s, with two championship final appearances, defeating SU Agen in the 1943 final at Parc des Princes in Paris and losing the 1944 season final to Perpignan.
The following decades were less successful, and the club would have to wait until the 1980s to reach another championship final. In 1980 they contested the final of the Challenge Yves du Manoir, defeating AS Béziers 16–10 to win their second title in that competition. They made it to the championship final in the 1982 season, but were defeated by SU Agen, 18–9.
Aviron Bayonnais was relegated to the Group A2 in 1996, where it spent eight seasons. Following promotion to the Top 16/14 in 2004, they remained in the top flight for 11 consecutive seasons. The team was relegated to the Pro D2 in 2015, and has been a yo-yo club since then. In the 2021–22 Rugby Pro D2 season, they were promoted after defeating Stade Montois 49–20 in the playoff final.