Are there nonstop flights from Rhodes (RHO) to Bari (BRI)?

Yes. Ryanair fly this route. Flight time is about 1h 49m.

What is the fastest connection from Rhodes (RHO) to Bari (BRI)?

via Kos ≈ 2h 19m, via Mykonos ≈ 2h 19m, via Athens ≈ 2h 19m (estimated flying time, excluding layovers).

from 15,000 ANA miles (economy, one way, based on the published award charts).

Rhodes International Airport "Diagoras" (RHO) to Bari Karol Wojtyła International Airport (BRI)・1,113 km

Nonstop flights available (1 airline). Flight time about 1h 49m. Nonstop return flights also operate.

With milesANA 15,000 miles+ (via ATH)Economy, one way, estimate. Tap a connection for miles by cabin.

26 one-stop options, sorted by estimated flying time. Tap one to see the airlines on each leg and booking links.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.