Best time to visit Bhutan depends on your exact destination. Usually, the northern part of the country where the Himalaya lies is covered with snow throughout the year.
The southern part has a tropical climate while the eastern part is warm and dry. The western part during the monsoon receives heavy rainfall.
Most of the tourists visit Bhutan from September to December as the sky is clear and the weather is pleasant. It is the right time to catch a glance of the rare black-necked cranes, seen in Phobjikha Valley between late October and mid-February.
From June to August, it is monsoon season and the eastern, southern and western (heaviest rainfall) part receives heavy rainfall. The northern part is covered with monsoon clouds. It is cold during January-February, and most tourists avoid that time of the year.
If you want to enjoy rhododendron blooms, you can visit between March-April. Also, during the time the weather is dry and pleasant. You can still see the rhododendron in May, but the climate is hot and humid which makes traveling difficult.