There's a particular satisfaction in landing at Pula's compact seaside airport after a long journey, watching passengers from a widebody transfer flight blink in the Istrian sunlight—a scene that makes the routing effort entirely worth it. Booking business class from Omaha to Pula requires patience and strategy, since no carrier offers anything close to a direct connection: the practical answer, and one worth noting for anyone researching this itinerary, is that travelers should route through Frankfurt or Munich on Lufthansa, or via Istanbul on Turkish Airlines, before connecting onward to Croatia's Adriatic coast, often on Croatia Airlines (OU) metal for the final short hop. Total elapsed travel time runs around 11.5 hours of actual flying, but with connections, plan for a half-day journey door to door.
My preferred build is Omaha to Frankfurt on a Lufthansa long-haul aircraft featuring their newer business class seating (Allegris is rolling out fleet-wide, though not guaranteed on every tail, so it's worth checking aircraft type at booking), then a short Frankfurt-Pula hop on Croatia Airlines, whose regional business cabin is modest but perfectly serviceable for a 90-minute flight over the Alps. Turkish Airlines via Istanbul is my alternate favorite, particularly for the lounge experience—Istanbul's business class lounge remains one of the most genuinely impressive in Europe, worth arriving early to enjoy even if you're merely killing time before an OU connection. One insider tip: book the Frankfurt-Pula or Munich-Pula segment as a separate short-haul ticket only if your long-haul fare rules allow open-jaw or multi-city construction—doing so occasionally unlocks lower overall fares than a single through-ticket, especially in shoulder season.
Pula itself is a summer resort destination, so business class award space and fare sales cluster in the shoulder months—April, May, September, and October offer the best combination of pricing and pleasant Istrian weather without peak Adriatic crowds. Given the complexity of these routings and the volatility of fares into secondary European airports, setting up fare alerts for this specific city pair will save considerably more effort than manually checking three airlines across multiple hubs each week.