You can find frequent buses running between Siliguri and Phuentsholing or Jaigaon. These bus services are operated by Royal Bhutan Government. From Phuentsholing, you can find taxis and buses to Thimpu. So, you can get a direct bus to Bhutan but have to change the bus after reaching there to reach other areas such as Thimpu.
Hi Maria! There is a frequent bus service between Siliguri and Phuentsholing/Jaigaon( Bhutan). It is operated by the Royal Bhutan Government. It is a roughly 4 hour journey, and departs from the bus station near The Heritage Hotel, two times a day.