What are my options for doing wine tasting in the Rioja area without a car. Is there a bus from Bilbao to Laguardia?
The public transportation I'm familiar with is a bus linking Vitoria-Gasteiz to Logrono, Line 9. That bus stops in Laguardia. The operating company is Alava Bus or Araba (I'm confused), and there are several buses a day. No more than one or two of them would work for someone beginning the day in Bilbao, because it takes some time to get from Bilbao to V-G. You can download the schedule from the webpage I linked to.
However, it turns out there's a once-a-day useful-for-day-tripping option from Bilbao (Line 17) to Logrono, also stopping in Laguardia. It shows up on the same website as the V-G/Logrono bus, and again you can download the schedule. Departure is at 9 AM; arrival, at 10:42 AM. The return leaves Laguardia at 7:53 PM and reaches Bilbao at 9:35 PM. Best to confirm all details once you're in the area.
I should perhaps mention that one Sunday I waited fruitlessly in Ripoll (Catalunya) for the only direct bus of the day back to Girona. The bus never showed up. I paid for two hotel rooms that night. I would be nervous about having only one bus available to take me back to Bilbao. There's also a 2:09 PM bus from LaGuardia to Vitoria-Gasteiz, but the V-G transfer will make the trip take longer.
A car would be very helpful here.
Even if you manage to get from Bilbao to Laguardia on a bus (you have to get to Vitoria-Gasteiz or Logroño first, and then to Laguardia), there are just three wineries in Laguardia and, in my opinion, just one of them is interesting (Casa Primicia). For the rest of wineries you´d need a taxi or a driver, as they are quite far apart. Wine is very good in all bars in Bilbao and very cheap, normally less than 2eur a glass, so if you want to taste wine, I´d go bar hopping (over 3000 bars in Bilbao for a population of 354,000 thousand).