That was until the final few minutes of the half, when Ibai struck the crossbar twice, first after bursting into the box and then with a free kick.
In the second half Bilbao upped the tempo again and forced a penalty in the 58th minute when Susaeta was brought down in the box. Benat stepped up but was denied by Sara.
The Betis goalkeeper produced an even better save shortly afterwards, tipping Susaeta's curling effort around the post, before, against the run of play, Betis shocked the home crowd.
The visitors broke away and when the ball found Jorge Molina in the box, the striker scuffed his second attempt into the goal for an unlikely lead.
Ten minutes later Bilbao were level. Substitute De Marcos found space at the back post and headed past Sara from Benat's delivery.
The turnaround was then completed by another header, this time from San Jose who rose highest to power in Ibai's cross.
Betis gave the hosts a scare with two minutes remaining when Molina raced clear, but he could only find the outside of the post with his curling effort.
The home side saw the game out though for a deserved victory which moves them up to fourth place.