The hosts could have moved to within three points of Real Madrid in third with victory tonight and Ruben Castro put them on their way with his second-minute opener.
Another Herrera effort, which drifted wide of the post, came minutes before their equaliser, which came courtesy of Aritz Aduriz.
The Spanish forward collected a precise Herrera pass and dinked the ball over the onrushing Adrian to give Bilbao half-time parity.
Athletic had several chances in the second period and could have snatched maximum points late on when Adrian superbly denied Oscar de Marcos a stoppage-time winner.
Betis remain in fourth, but have now won fewer than half of their home matches.