As a Bilbao local: there´s no train from the airport to the city, there´s a bus (3eur) every 20min that stops a 5min walk from the Guggenheim. Taxi should be around 30 to 35eur.
If you´re renting a car at the airport (any particular reason for doing so? The same rental companies can be found in the city), driving into Bilbao is easy (it´s a very compact city, we walk everywhere, no need at all for a car while in the city). There´s a parking lot at Plaza Euskadi, a very short walk to the Guggenheim.
Do NOT miss the old quarter of Bilbao, a beautiful area, as the rest of the city (you´ll love its architecture). Plenty of good restaurants, from several Michelin ones to a wide variety of cheaper ones...budget? Preferences?
I would not rent a car for Bilbao, public transport is excellent in the Basque Country and driving and parking in the city may be complicated, as there´s currently a "war" against combustion engine vehicles and speed limit is just 18miles an hour.