There are at least three camino routes from Bilbao to Portugalete. The "official" route is ~19km and goes away from the estuary and over some hills. The two alternate routes are ~13km and along either side of the estuary (the waterway from Bilbao to the Atlantic that's ~15km long) and we followed the eastern (right-hand) side of the estuary.
We walked on the opposite side of the estuary from downtown and the Guggenheim was opposite us - a very unique design and we will visit when we return next month.
The first few kilometers were quite nice and on a wide sidewalk with space for walkers, runners and bikers. However, it eventually turned into a normal sidewalk and then into a rather narrow space on the edge of the road. We arrived Portugalete, perhaps a few kilometers from the Atlantic, and crossed on a rather unique "hanging bridge" - imagine a small barge-like "ferry" for passengers and cars that's suspended by cables (~30' above the water) from a set of girders hight above and cross the river.
After arriving Portugalete, we saw two fellow pilgrims, brothers from Finland, and had lunch at the same cafe along the estuary. Then we walked up the hill and to Pension Buenavista, a rather modest place but certainly adequate and inexpensive.
Downtown Bilboa and the estuary
Views of the Guggenheim museum - above and below