Air:
The most convenient way of entering Bhutan is by Druk Air (National Carrier) or Tashi Air (Pvt. Airlines), Airbus A319. As flights can be delayed due to weather conditions (particularly during the summer months), it is advisable to allow 24 hours before any onward connection. The following stations are connected with Druk Air / Tashi AirFlights:

India (Kolkata, Bagdogra, Delhi, Gaya, Mumbai, Guwahati)
Nepal (Kathmandu)
Thailand (Bangkok)
Bangladesh (Dhaka)
Singapore

Both airlines flies several times a week between each destinations, but flight timings and frequency vary according to season. 
Kindly check their websites :
– Druk Air www.drukair.com.bt
– Tashi Air www.bhutanairlines.bt

Land:
Arrival/departure through the south-western border town of Phuntsholing, south- central border town of Gelephu and the south-eastern border town of Samdrup Jongkhar.

The nearest airport to the south-western border town of Phuntsholing is at Bagdogra, West Bengal, about 4 hours’ drive away. Phuntsholing is a convenient entry/exit point for tourists wishing to visit the Indian states of Sikkim and West Bengal along with Bhutan.

Domestic flights:
Bumthang airport in central Bhutan and Yongphula airport in Trashigang in the East are now open. For domestic flights and fares click here

The nearest airport to the south-eastern border town of Samdrup Jongkhar is at Guwahati, capital of the Indian state of Assam, about 3 hours’ drive away. Samdrup Jongkhar is a convenient entry/exit point for tourists wishing to visit the Indian states of Assam and other North Eastern states of India along with Bhutan.