The Basque side spurned a penalty opportunity when Benat Etxebarria failed to convert from the spot, and they fell behind just after the hour when Jorge Molina tapped in from a corner.
But Oscar de Marcos headed in an equaliser before Mikel San Jose grabbed the winner with eight minutes to go to make it four wins from six under former Valencia boss Valverde.
Having made the stronger start to the season, it was little surprise that Bilbao made the better start, with Markel Susaeta and Ander Herrera failing to convert presentable chances.
Betis slowly settled, and striker Chuli out to have done better with a right-footed shot when he was found in the box by Salva Sevilla.
Herrera then spurned two excellent chances at the other end, twice heading straight at Guillermo Sara in the Betis goal from close range, before Ibai Gomez struck the bar, ensuring the game remained goalless at the break.
Bilbao's best chance yet arrived 12 minutes after the break after Susaeta was fouled by Xavi Torres in the box, but Benat's penalty was saved low to his right by Sara.
And just five minutes later the hosts were behind. A corner was allowed to run across the six-yard box and Molina was on hand to turn the ball in.
The lead lasted just 11 minutes as Benat made some amends for his penalty miss by delivering the cross for De Marcos to net the leveller.
The turnaround was then completed when San Jose struck from a Gomez corner.