There's no nonstop way to bridge the Rio Grande Valley with the Norwegian fjords, which is precisely what makes routing decisions the whole game when booking business class from Albuquerque to Bergen. In practice, this means one connection in the US followed by a European hub transfer, since no carrier flies ABQ direct to anywhere in Scandinavia. The most reliable itineraries funnel through Denver or Chicago onto a transatlantic partner, then into Copenhagen, Frankfurt, or Amsterdam for the final short hop up to Bergen. SAS via Copenhagen is my preferred routing for this journey — their A330 and A350 business class cabins offer proper lie-flat seats with direct aisle access on the widebody legs, and Copenhagen's compact layout makes for one of the easiest connections in Europe, especially with SAS's own lounge there. Lufthansa through Frankfurt is a close second, particularly now that select long-haul aircraft feature the new Allegris business suites, though not every frankfurt-bound flight has rolled these out yet, so it's worth checking the specific aircraft before booking. KLM via Amsterdam rounds out the trio, with their reliable World Business Class product on the 787 and A330 fleets and a Schiphol connection that's straightforward if occasionally sprawling.
Having flown this corridor repeatedly, my strongest insider tip is to build in a longer layover in Copenhagen or Amsterdam during summer rather than rushing the connection — Bergen's weather is famously unpredictable, and afternoon flights into BGO get canceled or delayed by fog and wind more often than the airlines advertise, so a tight 60-minute connection can unravel a whole itinerary. Arrive at your connecting hub with enough buffer that a missed final leg doesn't cost you a night in an airport hotel instead of a Bergen guesthouse.
Late spring through early autumn — May through September — consistently offers the best combination of award and revenue business class availability on this routing, since that's when Bergen's tourism season peaks and airlines add capacity on the short intra-European legs. Given how fare classes fluctuate across three different alliances and routing options, setting up automated fare alerts for this specific city pair is the smartest way to catch a business class release the moment it opens up.