The hosts almost broke the deadlock with two chances in quick succession in the 14th minute as Lionel Messi first set up Pedro to test Gorka Iraizoz before seeing a shot of his own denied by the Spanish keeper moments later.
They continued to push for the opening goal and almost got it four minutes later when Alexis Sanchez rose highest inside the box to nod a corner on, but Marc Bartra just couldn't reach the ball to convert.
Bilbao came within inches of taking the lead against the run of play shortly after the half-hour mark when Aritz Aduriz unleashed a spectacular bicycle kick that came back off the inside of the post.
Barca also hit the woodwork shortly afterwards as Pedro's drilled ball towards the back post was met by Sanchez, who somehow directed his shot onto the bar rather than over the line.
Iraizoz was again on hand to keep the scores level five minutes before the break, saving from Sanchez before also getting down well to deny Pedro moments later.
Neither side could find the opening goal before the break as the two teams went into the interval all square.