Are there nonstop flights from Milan (LIN) to Bari (BRI)?

Yes. ITA Airways fly this route. Flight time is about 1h 24m.

What is the fastest connection from Milan (LIN) to Bari (BRI)?

via Rome ≈ 2h, via Split ≈ 2h 1m, via Ronchi dei Legionari/Trieste ≈ 2h 4m (estimated flying time, excluding layovers).

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

Milano Linate Airport (LIN) to Bari Karol Wojtyła International Airport (BRI)・772 km

Nonstop flights available (1 airline). Flight time about 1h 24m. Nonstop return flights also operate.

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

18 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.