Are there nonstop flights from Varna (VAR) to Bari (BRI)?

No. The fastest connection is via Sofia, about 2h 7m of total flying time.

What is the fastest connection from Varna (VAR) to Bari (BRI)?

via Sofia ≈ 2h 7m, via Belgrade ≈ 2h 19m, via Istanbul ≈ 2h 27m (estimated flying time, excluding layovers).

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

Varna Airport (VAR) to Bari Karol Wojtyła International Airport (BRI)・940 km

No nonstop flights. The fastest connection is via Sofia (SOF), about 2h 7m of flying time (layover not included).

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

None.

14 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.