Dubrovnik's medieval walls have a way of humbling even the most jaded transatlantic flyer, but getting there in comfort requires some routing savvy since no carrier flies nonstop between the two cities. There is no nonstop business class from San Francisco to Dubrovnik; the practical routing runs through United's hub network via Newark or Munich (on its Star Alliance partner Lufthansa's metal in some seasons), then a short connection onward to Croatia Airlines' Dash 8 or A319 service into DBV. Total journey time hovers around 13 hours in the air, but plan for 16-18 hours door to door once you factor in the connection. United's Polaris business class — lie-flat seats with direct aisle access on its 777s and 787s out of SFO — is the backbone of this itinerary, and I've found the Newark routing tends to offer more consistent widebody equipment than West Coast-originating alternatives.
American Airlines is worth watching too, particularly for those willing to route through Philadelphia or London, connecting onto partner metal for the final Adriatic leg. American's Flagship Suite on its 777-300ER, when available on the transatlantic segment, is among the better hard products in the U.S. fleet, though you'll still need a Croatia Airlines connection to finish the journey — their regional jets are narrow-body and functional, not luxurious, so treat that final hop as a formality rather than part of the "business class experience."
My insider tip: book the Munich connection whenever schedules allow, since it gives you access to Lufthansa's excellent business lounge for a proper meal before the final descent into Dubrovnik's compact, single-runway airport — arrival there is refreshingly fast, with bags often out before you've cleared passport control. April, May, September, and October are the sweet spot for this routing, both for weather in Dubrovnik and for fare softness before and after the Mediterranean cruise crowds peak. Given the multiple routing options and partner airline variability, setting up fare alerts is genuinely the smartest way to catch a strong business class fare on this itinerary before it disappears.