Druk Air

DRUK AIR is the only airline in Bhutan.  It has two Airbus A319, flying from and to Bangkok (Thailand), Kathmandu (Nepal), Kolkata (India), Dhaka (Bangladesh), Delhi (India), Bagdogra (India), Guwahati (Indai).
http://www.drukair.com.bt/

Usually, people take flight from Bangkok(BKK) to Paro(PBH).  During summer, there is 1 direct flight flying between BKK & PBH per week.

Sat  KB129  depart BKK at 08:45pm, arrive PBH at 10:45am
Fri   KB128  depart PBH at 12:15pm, arrive BKK at 16:15pm