There's no nonstop path connecting the Midwest to the heel of Italy's boot, so anyone booking business class from Kansas City to Bari needs to think like a route planner rather than a passenger. The honest answer to how you get there in comfort: fly Delta or connecting partner metal to a major European gateway, then drop down to Bari on a short intra-European hop, since Bari's airport (BRI) simply doesn't support widebody long-haul service. My preferred routing after dozens of iterations is Delta out of MCI to Amsterdam or Paris, transferring onto Delta or a joint-venture partner, then finishing on a regional carrier into Bari — or alternatively connecting through Frankfurt on Lufthansa, whose A340 and A350 business class cabins (and increasingly the new Allegris seat on select A350 routes) offer a genuinely restful lie-flat experience for the transatlantic leg. Alitalia's successor ITA Airways also serves the Rome and Milan gateways with A330 business class, which pairs nicely with a quick domestic Italian hop to Bari.
The real craft here is in the connection strategy. I've found that routing through Rome Fiumicino rather than Milan Malpensa shaves real stress off the final leg into Bari, since Fiumicino's domestic transfer process for arriving international passengers is more streamlined and gives you a cushion if your long-haul segment runs late — build at least two hours for that connection if you're transferring terminals. Lufthansa's Frankfurt hub is my second choice, particularly outside summer, when FRA's efficient B-gates make same-day connections onto Munich or Rome more forgiving. Seasonally, April, May, September, and October are the sweet spot for this itinerary: Puglia's shoulder season delivers ideal weather for exploring the Adriatic coast without the July-August crush, and business class award space on the transatlantic legs tends to open up more generously in those windows as leisure demand softens.
One insider trick: search availability into Naples (NAP) as a backup arrival airport — it's roughly two hours from Bari by car or train, and I've seen instances where premium cabin award seats clear into Naples when Bari-bound connections are sold out. Given how many moving pieces this itinerary has — three carriers, multiple fare buckets, and a seasonal sweet spot — setting up automated fare alerts for this specific corridor is far more reliable than manually refreshing search engines, and it's the method I rely on before locking in any booking to Puglia.