Getting around in Bhutan can only be done by road since no other mode of transport is available.
Intra-country flights do not exist, since Paro International Airport is the only operational Airport in Bhutan.
There are no railways in Bhutan.
The roads that run across the country are known for their twists, turns and steep inclines, but they are generally very well-maintained and safe. Local and inter-district bus services are not very comfortable and stop frequently. Your local travel agency and is likely to recommend going around in a car and even offer to book one for the duration of the trip.
There are no waterways in Bhutan.