Are there nonstop flights from Tashkent (TAS) to Batumi (BUS)?

Yes. Uzbekistan Airways, Flykhiva fly this route. Flight time is about 3h 12m.

What is the fastest connection from Tashkent (TAS) to Batumi (BUS)?

via Tbilisi ≈ 3h 43m, via Baku ≈ 3h 45m, via Mineralnyye Vody ≈ 3h 54m (estimated flying time, excluding layovers).

from 29,500 ANA miles (economy, one way, based on the published award charts).

Tashkent International Airport (TAS) to Alexander Kartveli Batumi International Airport (BUS)・2,298 km

Nonstop flights available (2 airlines). Flight time about 3h 12m. Nonstop return flights also operate.

With milesANA 29,500 miles+ (via IST)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.