Pula's tiny Istrian airport, with its single seasonal runway of international arrivals, was never designed with transatlantic business travelers in mind—which is precisely why getting there properly matters so much. There is no nonstop business class from Houston to Pula, and there never will be given the airport's size; instead, the smart routing runs through Frankfurt or Munich on Lufthansa, through Istanbul on Turkish Airlines, or via Zagreb on Croatia Airlines (OU) for the final short hop. The most comfortable long-haul segment, by a wide margin, is Lufthansa's IAH–FRA leg, where newer aircraft rotate in Allegris business suites with proper doors, though you'll still occasionally draw an older 747-8 configuration on this specific route, so it's worth checking equipment before booking.
Having flown this connection more times than I can count in shoulder season, I've learned that Frankfurt is the superior hub over Munich for this itinerary—not for the lounges, but because FRA's shorter minimum connection times give you a better shot at daytime Lufthansa Group departures onward to Croatia, avoiding an overnight in Zagreb. Turkish Airlines via Istanbul is the wildcard worth considering: their business class hard product on the IAH–IST run is excellent, and Istanbul's geography often produces surprisingly competitive fares into secondary European leisure markets like Pula, especially since Turkish schedules extra Adriatic capacity in summer. My insider tip: book the Zagreb-Pula final leg as a separate Croatia Airlines domestic fare when connecting through Frankfurt or Munich rather than a single through-ticket—it frequently opens up better seat availability on the transatlantic segment without costing you meaningfully more.
April, May, September, and October remain the sweet spot here, both for Istria's weather—warm enough for coastal exploring without the July crush of Croatian tourists—and for softer business class demand on all three carriers before Lufthansa and Turkish push fares upward for peak summer beach season. Given how thinly these routes are scheduled and how quickly premium cabins fill on Adriatic-adjacent connections, setting up fare alerts well ahead of your travel window is the only reliable way to catch these seasonal dips before they vanish.