This can be done, but is going to be a long and hard day.
Note that, from Goikoletxea (about 1.5 km before Larrabetzu), you will be walking on asfalt/concrete (with practically no shade) until you reach the base of monte Avril.
Just before arriving to Zamudio, there is an alternative to your left via the underpass, which saves you some asfalt (and time) and circumvents Zamudio.
There are buses from Larrabetzu every hour on working days.
Check here (sorry its in Spanish and Basque only) for A3223, which sometimes also starts from Goikoletxea. Also, there is another bus (A2151) which will take you directly to the hanging bridge, but on the other side of the river from Portugalete.
If you are adventerous, you could try an alternative path from Lezama to Bilbao with less asfalt.
Somethig like what appears in this track.
This morning I saw 3 people near Zamudio walking the camino. The season is starting...