You have three options that i know of to get to Portugalete, take the official camino (18km from the center of Bilbao), walk the eastern side of the river(12km), take a metro.
I was told by the hospitalero at the altamira albergue in bilbao to take the route which follows the eastern side of the river to the sea and cross at Portugalete, he said that the official camino goes all over the place, up and down before it gets to where it meets the alternative route. Being a good boy, i duly follwed his advice, what i would say is that add 2 km to the the eastern side route as you backtack from the albergue de peregrinos, take 2km off the official route, the albergue is already well into that way. The eastern side is all asphalt urban walking, very flat, the highlight being crossing back over the river on the gondolier bridge, the way i went had a dangerous section for about 1km just before i got to the crossing, there may have been another way parrallel to mine with pavements a block or two back from the river. I did not see any signs, i may have taken the wrong line, but one thing i do remember is on the dangerous section i heard someone beeping their horn at me,it was the hospitalero giving me a big smile and waving at me, I grimaced back at him with a half hearted wave.
Mike