Hi Vikas, June, July and August are monsoon months in Bhutan and neighboring Indian states. Not only will it be difficult to drive, but you won't be able to enjoy nature and other attractions due to torrential rain. There is also an off chance of landslides. Best time to do a road trip to Bhutan is from March to May and September to October.
Read the article carefully and you would get a contact number of Bhutanese local tourist guide, Sonam Dorjx at the bottom of the article. If you need you can contact him.