I crossed the river in the gondola for 3 euros. I travelled by local train from Bilbao Abando station to Portugalete enjoying a spectacular view of the bridge while approaching Portugalete station. Having crossed the bridge I went to the nearby Areeta metro station to catch a train back to Bilbao and the Guggenheim Museum.
I believe that this is the world's last remaining operating transporter bridge; I have only seen one other, derilict at La Boca in Buenos Aires, Argentina.