Access
There are only two entry points to Bhutan: most travelers arrive by air at Paro, some arrive by road at Phuentsholing on the southern border with India. In any event you have to fly by the national carrier, Druk Air, either in or out. Druk Air has no agreements with other carriers so you will need to arrange your own ticket to and from wherever you connect with them as they operate the only airline that flies into Bhutan. The flight from Kathmandu to Paro provides the most dramatic view of Himalayan scenery of any scheduled flight. Be sure to get a window on the left side for maximum visual effect.
Druk Air won't issue your ticket until they have received your 'visa clearance' from DOT. Without competition they can afford to be expensive, and they are. On arrival at Paro airport, the clerk will miraculously find your clearance and issue your visa, and then away you go.
Another way is to plan a trip by road, starting in Kathmandu, perhaps visiting Darjeeling and Sikkim en route and enter Bhutan by the border Bhutanese town of Phuentsholing.