You can get to Bhutan by Air from Katmandu, Delhi, Kolkata, Dacca, and Bangkok, Singapore, Guwahati, Bagdogra. All these routes are chiefly operated by Druk Air, which is government run Airline, since October 2013, the private owned Bhutan airline, started its operation also. There is at least one flight operating daily (Round Trip) by both companies from Bangkok. For other routes, it is confined to few days in a week. Moreover it’s subjected to frequent change in schedule. In order to have exact idea of the schedule, Please refer to Airlines websites
If you opt for Overland options, entry to Bhutan is well connected with network of road from India. Transports are available from Indian cities of Siliguri, Darjeeling, Sikkim and Kalimpong, Guwahati. There are 3 entries and exit point, the most commonly used is the southern commercial town of Phuentsholing, the others are mid-south town of Gelephu and sleepy Far East town of Samdrup Jongkhar.