Bilbao's Guggenheim crowd and Basque food pilgrims have quietly made this one of the more interesting connecting puzzles in transatlantic travel, since no carrier flies nonstop between the two cities. There is no business class from San Francisco to Bilbao that skips a connection, so the real decision is which European hub you want to be routed through: Madrid via Iberia, London via British Airways, or Frankfurt/Munich via Lufthansa. My preference, after years working this itinerary, leans toward Iberia's Madrid connection, since it's a domestic-feeling short hop into Bilbao and Iberia's A330 business class (lie-flat seats, direct aisle access on most configurations) makes the long SFO–MAD leg genuinely restful. British Airways routes through Heathrow, where their Club Suite — with its sliding door and forward-facing lie-flat seat — is currently one of the best hard products in the sky, though the T5 connection can add time if you're not careful with layover buffers. Lufthansa's Frankfurt or Munich routing suits those wanting to sample the airline's newer Allegris cabin, though it's not yet guaranteed on every SFO frame, so it's worth checking aircraft type before booking.
The insider move here is to fly the long SFO-to-hub leg overnight and treat the short intra-European connector as a "reset" segment — grab a shower in the Iberia Business lounge at Madrid's T4 or BA's Galleries First lounge at T5 before the final descent into Bilbao's compact, easy-to-navigate airport, which clears passengers quickly even during Semana Grande in August. Seasonally, January through March and again in October and November are the sweet spots for this routing, both for fare softness and for avoiding the peak Basque tourist surge.
Because pricing on this three-airline, three-hub route fluctuates more than most transatlantic itineraries, setting up fare alerts is the smartest way to catch the inevitable dips before they vanish.