There is an aire listed in campercontact at 43°15'34.6"N 2°57'48.7"W
It is 15 euros per night and has full services.
HOwever. There is an adjacent free car park where we have stayed overnight without problem but obviously no services.
The advantage of this location is that there is a bus stop only a few metres away which will take you right into the city centre.
The location is on top of a hill overlooking the city and you can actually see the Guggenheim museum which is well worth a visit and Its a pleasant walk along the river after getting off the bus.
I posted on another forum, a similar question. Here's one of the replies.
(there are two camperstops in Bilbao, one at the hostel and one right up at the top overlooking Bilbao, both have got a bus that stops outside, we had been to Bilbao twice but both times didn't stay so last year made a big effort and stayed three nights, the city is beautiful, and the museum is breath taking from the outside, don't know what was on but we couldn't go inside, but still amazing just from the outside.
they are both in campercontact)
You can search campercontact on google.
We will be stopping there Thursday/Friday night.
If you're waiting at the Port, the Metro runs from Santurzi to the city centre. A few years since I spent time there, but I found it a fascinating city, particularly the old town the other side of the river.