Hi chinalil! Welcome to the forum!
I don't know how busy are buses on that route so I don't know how advisable would be to book in advance. However, I'd like to tell you that I think the Alsa buses don't stop at the airport. You would need to get a bus from the airport to downtown Bilbao and the Alsa one from downtown Bilbao to Irún. Alternatively, you could take a bus straight from the Airport to San Sebastián (aka Donostia) with Pesa (
www.pesa.net) and another one from San Sebastián to Irún with
http://ekialdebus.eus (that would mean a short walk in San Sebastián because buses from San Sebastián to Irún make different stops in San Sebastián than the ones arriving from Bilbao airport). There's frequent service from Bilbao airport to San Sebastián and even more frequent from San Sebastián to Irún.
From San Sebastián to Irún, train would be another option. Take a look at
www.renfe.com for the train schedules (be sure to check the Commuter trains Schedule because those trains aren't showed on the general Schedule as well as aren't showed on the booking area because you can't book them in advance). The train station used by RENFE is really close to the bus station.
www.euskotren.eus is another option to go by train from San Sebastián to Irún but the walk to the closest euskotren station is more or less the same than the walk to get the bus I quoted above so if you are looking for avoiding walks, to take a RENFE train would be your best bet.
In other words, if you decide to take the direct bus from Bilbao airport to San Sebastián and you want the shortest walk in San Sebastián to take other transport to reach Irún, go to the train station used by RENFE and take a Cercanías train to Irún. If you don't want to take the direct bus from Bilbao airport to San Sebastián, you can also take a bus from Bilbao airport to downtown Bilbao and an Alsa bus from downtown Bilbao to Irún.