Point of entry & exit to Bhutan by air is at Paro, which is in the western region of the country. If arriving overland, the points of entry/exit are at Phuentsholing, Gelephu and Samdrup Jongkhar in the southern region that connects Bhutan with the Indian states of West Bengal and Assam respectively.
There are two airlines operating in Bhutan i.e. Druk Air, the national airlines which has been in operation since 1982 and Tashi Air which launched its international operation in 2012. Bhutan’s only International Airport is located in Paro, at an altitude of 2400 Mtrs./7,300 ft. height which is also day light restricted; besides there are three domestic airports located each in central, eastern and southern Bhutan. As of now, Bhutan is connected to & from Bagdogra, Gauwhati, Bodh Gaya, New Delhi, Kolkata and Mumbai in India; Kathmandu in Nepal, Bangkok (Thailand), Dhaka (Bangladesh) and Singapore. The flight between Paro and Kathmandu is one of the most stunning as the aircraft passes over four of the five highest mountains in the world; in a clear weather, one can have spectacular views of Mt.Everest, Mt.Lhotse, Mt.Makalu and Mt.Kangchenjunga.
Druk Air: https://www.drukair.com.bt
Tashi Air: http://www.bhutanairlines.bt/; http://www.tashiair.com
If you are reaching/exit Bhutan overland, you will have to enter/exit either through the border town of Phuentsholing in western Bhutan or Gelephu in the southern part or Samdrup Jongkhar in eastern Bhutan. Phuentsholing is 180 km from Bagdogra Airport in West Bengal and takes around 5 hours to reach Phuentsholing. Gelephu in southern Bhutan is another entry point. Samdrup Jongkhar is another entry point to Bhutan from the eastern region. It is approximately 150 km from Guwahati Airport in Assam and takes around 4 hours to reach.