To visit the Vizcaya Bridge from Bilbao center, it will take about three or four hours. It is possible to go by bus: it leaves from the center of Bilbao and has a stop at the Vizcaya bridge. You can also go by metro. The journey time is about 20 minutes.
It is also possible to visit the Bridge and walk across, at a height of 50 meters. The price is 8 euros.
The visit is well worth it as they give you explanations about its construction and the truth is that it is very quirky. Once there, you can visit Getxo, with its old port and its cliffs. It has a beautiful promenade by the sea and the beach of Ereaga, very crowded in summer and full of walkers.