The Kingdom of Bhutan is an isolated country in Southern Asia. In the North it is bordered by the huge Himalaya mountains with a not exactly clear border to the region of Tibet, China. In the South it borders India.
There are no highways in Bhutan. Most roads are going through the mountains and they are hardly straight. There ist not much private traffic in Bhutan because most people do not own vehicles. But thats may be a reason why hitchhiking is very common there. But because of the low traffic, the roads through the mountains and an opinion that everything has to be done slow, you will need some time, even for small distances.
It difficult for foreigners to get in. For individual travellers it seems to be very hard to get in, because you need to have an organised trip by an agency, you must pay high travelling taxes and you will need a guide, otherwise you won't get a visa.
Since 2008, Bhutan has a new young king who might change the situation a bit. So keep updated.
There is a nice film called "Travellers & Magicians" which gives you a feeling how hitchhiking in Bhutan might feel. Travellers & Magicians