The answer
Walk out of arrivals and take the Bizkaibus A3247 — €5 for an occasional ticket, 20–25 minutes to Gran Vía, Plaza Moyúa and Termibus, roughly every 15 minutes.
Bilbao has no metro and no train to the airport, so the A3247 is the only public transport link — and at €5 it is a fifth of a taxi to the same place.
Tight budget? A Barik card turns the identical ride into the ordinary zone-2 fare, €1.19 — but the card is not sold at the airport, so buy one at a Metro station once you reach the city.
Three or four of you with bags? A taxi is €27 on a working day and €30 on a public holiday to central Bilbao, so the bus still wins.
⚠️ The traps (walk past these)
There is no metro and no train to this airport
Bilbao Metro does not serve Loiu, and neither does Renfe or Euskotren. The A3247 bus is the only public transport link between the airport and the city. Plenty of guides still describe a 'metro to the airport' that has never existed.
Do this: look for the Bizkaibus A3247 stop outside arrivals and ignore any Metro sign
The €5 ticket is the tourist price
Bizkaia's own notice confirms the €5 occasional ticket on the A3247 is the price for people without a Barik card. Validate a Barik card instead and the same journey costs the zone-2 Creditrans fare of €1.19 — a saving of €3.81 a head, each way.
Do this: if you are in Bilbao more than a day, buy a Barik card in the city and use it for the return to the airport
Barik cards are not sold at the airport
The Bizkaibus desk on the arrivals floor can only recharge a Barik you already own. Arriving without one means paying €5, and the €1.19 fare is out of reach until you get to a Metro station in town.
Do this: buy the Barik card at a Metro Bilbao vending machine in the city, not at the airport
Nothing runs in the small hours
The last A3247 leaves the airport at about 23:40 in summer and around midnight in winter, and there is no night service at all. A 2am arrival has the taxi rank and nothing else.
Do this: for an arrival between 00:30 and 05:00, plan on a taxi or a pre-booked transfer
The taxi rate changes on holidays
Aena's indicative fare to Bilbao rises from €27 on a working day to €30 on a public holiday, and Termibus from €32 to €35. Drivers who quote one flat 'airport price' regardless of the day are not using the published tariff.
Do this: check the working-day or holiday figure on the Aena list before agreeing a fare, and ask for a receipt