The visitors had the first chance of the match, as Raul Garcia pounced on a loose ball outside the Sociedad penalty area, but his effort flashed wide of the goal.
The hosts came close to taking the lead on 28 minutes, as David Zurutuza found Sergio Canales with an inviting pass, but the former Real Madrid midfielder's effort was deflected over the crossbar by Xabier Etxeita.
After the break the hosts came close to opening the scoring when Zurutuza found Canales in the penalty area, but his effort went narrowly wide.
Aduriz carved out a one-on-one opportunity with Geronimo Rulli minutes later, but the Sociedad keeper produced a good save.
The hosts came close to finding a goal on 81 minutes as Xabi Prieto found the head of Agirretxe with a cross, but the striker's effort was comfortable for Iraizoz.
Athletic Bilbao survived a late onslaught before the final whistle, as Iraizoz made two point-blank saves following a Bruma cross, before substitute Jonathas forced a low save from the Bilbao veteran.