Ljubljana rarely appears on the same sentence as "business class," which is precisely why the routing deserves attention: there is no nonstop option from Dulles, so every business class from Washington Dulles to Ljubljana itinerary connects through a major European hub, typically Frankfurt or Munich on Lufthansa, Paris-Charles de Gaulle on Air France, or Istanbul on Turkish Airlines. Lufthansa's Dulles departure puts you on a widebody with lie-flat business class seating (increasingly the new Allegris cabin on select aircraft), feeding into a short intra-European hop where Lufthansa's efficient short-haul business product gets you into Ljubljana's compact Jože Pučnik Airport with minimal fuss. I've found the Frankfurt connection the most reliable for tight winter schedules, since Munich's satellite terminal can eat your buffer time if weather rolls in.
Turkish Airlines via Istanbul is the wildcard worth considering: their long-haul business class, complete with the celebrated Turkish Airlines catering and lounge experience at IST, turns a connection into part of the trip rather than a chore, though the total routing time runs longer than the Lufthansa or Air France alternatives. Air France routes through Paris, where their business cabin on the Dulles sector (La Première aside) delivers solid width and service, and CDG's Terminal 2E has matured into a genuinely navigable connection point if you allow at least 90 minutes. My insider tip: book the Ljubljana feeder flight as a separate short-haul business fare only when the through-fare doesn't include it in premium cabin — some carriers price the regional leg in economy by default even on a business class ticket, and a quick call to reissue nets you a proper seat for the final hour.
Deal season here runs January through March and again in October and November, when leisure demand to Slovenia's ski regions and Lake Bled hasn't yet peaked and business travel between Washington and Central Europe is comparatively quiet. Given how thin capacity is on this city pair, setting up fare alerts is genuinely the smartest move you can make before committing to dates.