Rhodes rewards the patient traveler, and after a dozen or so crossings on this itinerary, I can say with confidence that there is no nonstop option worth waiting for: business class from Washington Dulles to Rhodes always routes through a major European hub, typically Frankfurt or Munich with Lufthansa, Heathrow with British Airways, or Athens with Aegean. Total journey time hovers around 11.5 hours in the air, though with connections you should budget closer to 14-16 hours door to door. Lufthansa's Allegris business class, now rolling out on select long-haul aircraft, offers a genuine upgrade over the airline's older product, with a proper door and improved seat privacy, while British Airways passengers connecting through Heathrow will find the Club Suite—with its sliding door and direct aisle access—a comfortable way to bridge the Atlantic before a short Aegean or BA hop down to Rhodes.
The insider move here is routing through Athens on Aegean Airlines for the final leg rather than flying into Rhodes via a second European connection on your primary carrier. Aegean's business class on the Athens-Rhodes sector, while a regional product rather than a flat-bed experience, is refreshingly efficient, and landing in Athens gives you the option of a deliberate overnight break at a hotel near the airport to reset before the short island hop—something seasoned Aegean travelers do routinely but that most itinerary planners overlook. Arriving into Rhodes itself, the airport is compact and manageable, so there's little upside to arriving red-eye; a midday arrival lets you clear customs and reach your hotel while daylight still favors that first glimpse of the Old Town.
Shoulder season—April, May, September, and October—is when this routing shines, both for softer demand into the Aegean and for noticeably better business class availability out of Dulles on Lufthansa and British Airways metal. Given how much fare and award space fluctuates on this three-airline, hub-dependent route, setting up automated price and availability alerts is the smartest way to catch the openings before they disappear.