There's no nonstop way to bridge a Pacific volcano-fed island and a Basque coastal city, and that's precisely what makes routing decisions the most important choice you'll make on this itinerary. Business class from Honolulu to Bilbao always requires at least two connections, since none of the three carriers serving this corridor—Iberia, British Airways, and Lufthansa—operate anything close to nonstop from HNL. My preferred routing runs through Los Angeles or San Francisco to Madrid on Iberia, whose A330neo business class delivers direct-aisle-access suites with real doors, followed by a short Iberia or Vueling hop to Bilbao. Alternatively, connecting via London on British Airways lets you experience the Club Suite on the transatlantic leg, though you'll want to double-check your onward connection to Bilbao operates via the same terminal to avoid a Heathrow shuffle between T5 and T3. Lufthansa routings through Frankfurt or Munich are worth considering too, particularly if Allegris-equipped aircraft happen to be flying your specific transpacific segment—though Allegris rollout remains uneven, so I always verify the exact tail number before booking.
Having flown this corridor numerous times, my strongest insider tip is to build in a deliberate overnight in your hub city rather than chasing a tight same-day connection—Madrid, in particular, rewards this with Iberia's dedicated business lounge and a chance to reset before the final Bilbao hop, which spares you the indignity of a red-eye-to-regional-jet grind after 13-plus hours in the air. Arriving into Bilbao's compact, Calatrava-designed airport is refreshingly civilized after the long haul, with bags typically appearing well before you've cleared the terminal.
Seasonally, January through March and October into November consistently offer the softest business class fares on this Pacific-to-Basque routing, as both leisure demand to Hawaii and peak European travel taper off simultaneously. Given the multi-carrier, multi-connection nature of this journey, fares shift often and reward patience—setting up automated fare alerts across Iberia, British Airways, and Lufthansa is the smartest way to catch a premium seat at its best value before it disappears.