The cheapest way would probably be to take a bus. It was less than 10 euros at the end of 2009 and only took an hour.
There is also the Euskotren train network (map: http://0.tqn.com/d/gospain/1/0/u/T/-/-/bilbaotram.jpg ) which would be faster. This is not the usual Renfe train network like the rest of Spain. It is private lines so Eurail passes dont work
You can also rent a car and drive down the highway (A8). It probably takes 40 mins or so. There are tolls on the highway so your costs also include fuel and toll fees. almost 9 years ago