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.
There are also two trains per day Logrono-Bilbao on Saturdays (11:25 and 19:38 - check on Renfe website). The train takes 30 mins longer than the bus, but tickets are fairly reasonable (right now prices are €11.25). Just in case you needed this info as a back-up plan!
Remember that the weekend of 8 April is the start of Holy Week in Spain, and as lots of locals will be travelling on the Saturday it would be wise to book in advance!