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. about 10 years ago