Mykonos rewards patience, and so does the routing required to reach it in comfort. There is no nonstop option connecting Colorado to the Cyclades, so business class from Denver to Mykonos always involves a transatlantic hop followed by a shorter European connector, with total journey time landing around 12.5 hours of flying once layovers are factored in. My preferred build is Lufthansa's Denver-to-Frankfurt segment, where the airline's Allegris business class has started rolling out on select long-haul aircraft, offering a genuine step up from the older business seats still found on much of the fleet — worth checking your specific aircraft type before booking. From Frankfurt, Lufthansa or Aegean Airlines can carry you onward to Athens, with a final short island-hop to Mykonos on Aegean's regional jets, typically in economy given the brevity of that last leg.
An alternative I've flown repeatedly is routing via London on British Airways, using their Club Suite — a proper door-equipped, direct-aisle-access seat now standard on their 777s and A350s out of Heathrow. Denver to London on BA's 787 or 777 gets you a slightly older but still comfortable Club World product, and connecting through Heathrow's Terminal 5 is efficient if you allow at least 90 minutes given the airport's sprawl. From London, BA or Aegean continues to Athens, then a puddle-jump finishes the journey. Athens International is the real logistical hinge point on this route — arrive with enough buffer for the walk between international and domestic terminals, especially in peak July and August crowds you'll want to avoid entirely.
That's precisely why April, May, September, and October are the sweet spot: shoulder-season Aegean demand is lighter, island ferries and flights run smoother, and premium cabin fares on the transatlantic legs tend to soften as summer beach traffic fades. Given how fragmented this itinerary is across three carriers and multiple alliances, fares fluctuate unpredictably — setting up dedicated fare alerts for this specific city pair is the smartest way to catch a favorable business class window before it closes.