The La Liga side fielded a side featuring many second-choice and B-team players although Igor Gabilondo and Alde Ustaritz both started for the Basque-only club.
Ligue 1 runners-up Bordeaux went ahead through a 19th-minute goal by former Manchester United and Sunderland striker David Bellion.
Midfielder Gabilondo levelled from the penalty spot six minutes later after forward Gaizka Toquero was fouled in the box.
French playmaker Yoann Gouffran put Les Girondins back in front with a superb solo strike on 33 minutes and the win was sealed for the title-challenging French team when defender Ustaritz put through his own net on the hour mark.
Athletic Club have seen a promising start to the season slip into another relegation dogfight after a run of eight games without a win left them two points above the drop zone.