There's a reason seasoned Aegean travelers treat Mykonos as a two-leg puzzle rather than a single booking, and cracking that puzzle well is what separates a miserable travel day from a genuinely enjoyable one. There is no nonstop option for business class from Nashville to Mykonos; the island's small airport (JMK) doesn't accommodate widebody service, so every itinerary routes through a European or Aegean hub before a short hop on Aegean Airlines or Olympic metal. The most reliable routing pairs BNA-London on British Airways or BNA-Frankfurt/Munich on Lufthansa, then a connection onward via Athens on Aegean Airlines (A3), whose short-haul business class is a simple but comfortable blocked-middle-seat product on A320-family aircraft. Total journey time hovers around 12.5 hours of air time alone, before factoring layovers, so this is very much a two-day-feeling itinerary even though it's booked as one ticket.
For the transatlantic segment, Lufthansa's Allegris business class—when you can secure it on the right aircraft—offers sliding doors and genuine privacy, a notable upgrade over their older long-haul cabins, while British Airways' Club Suite (rolling out fleet-wide but not universal, so check aircraft type before booking) gives you the enclosed-suite feel Americans have come to expect from premium international carriers. My personal preference after years flying this corridor is routing through London: Heathrow's T5 to T3 connections for BA metal are seamless, and BA's schedule aligns better with same-day Athens arrivals, letting you catch an afternoon Aegean flight into Mykonos rather than overnighting in Athens.
Shoulder season—April, May, September, and October—is when this itinerary shines, both for weather (Mykonos in August is a different, more chaotic animal) and for award and premium cash fare availability, since airlines shift capacity before and after the summer crush. My insider tip: book the Athens-Mykonos segment separately if Aegean award space disappears on your ticketed itinerary, then simply present your original ticket for onward check-in—gate agents rarely blink. Given how much these fares fluctuate hub-to-hub, setting up fare alerts for this specific routing is the smartest way to catch a rare dip before it vanishes.