For centuries, the different valleys of Bhutan were isolated from each other by torrential rivers and deep gorges. As a result, most of these valleys developed their own dialects. At present, there are about 13 different dialects spoken in Bhutan.
However, there are three major languages: Dzongkha, Sharchopkha and Nepali. Dzongkha is mainly spoken in the west, Sharchopkha in the east and Nepali in the south. News is broadcast in these three languages from the Bhutan Broadcasting Service in Thimphu.
Dzongkha is the national language of Bhutan. It has some similarity to Tibetan in speaking, while the alphabets are exactly same as Tibetan (but uses different style of scripts). It is also taught in schools and all students can speak Dzongkha and English. Although Dzongkha is a major subject in schools, English has taken precedence over Dzongkha in terms of students interest and their literacy, because most of the subjects like mathematics, science and geography are taught in English.
If you can speak English, you should not have much problem communicating in Bhutan. If you are in a town, you will see that almost everybody can speak English. However, if you go to remote villages, it will be helpful if you can speak little bit of Bhutanese.