Peaceable Projects Inc. is a U.S.-based non-profit group that brings the vast resources of the wide world together with the ongoing needs of the people who live, work, and travel on the Camino de Santiago pilgrim trail network in Spain.
There is an excellent bus service to Logrono from Bilbao (Termibus), several departures every day. Also, there is a bus from Biarritz/Bayona to Bilbao.
I have no actual details though, you must google a bit.
I am 51% convinced it would be the quickest way to use the bus connections, and not by train through Irun.
BTW, I would like to mention the excellent public bus services all over the Camino area. -Which is reassuring when you are afraid you might get into trouble while hiking, healthwise or other. There is always help and transport nearby.