Hi Emma,
At the moment, I have a note to myself to catch a bus at either 09.20 or 11.00 from Logrono myself (on 2 May), to return to Bilbao for a Dublin flight. However, looking at the La Union (bus company) website now, I think the Saturday departures from the Logrono bus station are at 08.30 and 11.00. The journey time is approx two hours. You may be able to buy a ticket online from the company, or just call into the bus station perhaps the evening before you want to travel.
Best wishes