I doubt if anyone has even actually been there from Kolkata. It takes around 4-4.5 hours from Siliguri or NJP station to Phuentsoling. A cheaper option is to go to Hasimara station from NJP station and then take a taxi to Jaigaon. This is a border town where you have to complete the formalities before being allowed to enter Bhutan. Taxis are available from Hasimara to jaigaon. Once past the border, scores of transport options available to take you to Thimpu and elsewhere. Also all in all 5-6 day trip can be covered in a maximum of 12-15k or even lesser.