Bilbao probed for the opener when Inaki Williams met a long ball from Raul Garcia, but he struggled to bring it under his spell as the chance fell away.
Barca shot-stopper Marc Andre Ter Stegen was called upon after 25 minutes to expertly tip a shot from Markel Susaeta over the top.
The visitors' first sight to goal arrived with seven minutes left in the first half, as Lionel Messi ventured forward to force a sterling save out of Iago Herrerin.
Leading to halftime, Garcia provided the final chance when his acrobatic effort was kept out by the busy Ter Stegen.
Barcelona signalled the early danger in the half, as Messi’s free-kick from outside the box sailed mildly over the bar on 54 minutes, with Arturo Vidal going close off a powerful strike.
Bilbao made the game’s first change, with midfielder Mikel San Jose replacing Benat Etxebarria on 57 minutes, while the Catalans responded with their first alteration, with Carles Alena taking the spot of Vidal.
Despite the limited offensive movements on either side, San Jose almost struck the ultimate blow on 66 minutes but his shot from the edge of the area narrowly missed target.
Luis Suarez drew up a response on 74 minutes with a similar effort that also drifted away from the intended position.
As Bilbao upped the tempo, Williams reappeared in the final eight minutes as he sent an effort wide of the mark after collecting a cross from the right.
Ter Stegen’s reflexes then came to the aid of the visitors to prevent another close-range strike from Williams, before the home side had Oscar de Marcos sent off for picking up a second yellow card late on.
The encounter ended goalless on the night as Barca only moved six points clear of rivals Real Madrid.