I plan to do this trip next year..Below is the itinerary that I have made for my future travel.. Before going to Bhutan, you have to obtain travel permit either from Kolkata or when you reach there, latter takes longer time..
tourist going beyond Thimphu and Paro need to acquire a 'special area permit' from the RGoB Immigration Office at Thimphu on any working days (Monday to Friday).
Plan to take a flight to Bagdodara. Take a cab from Bagdodara to Phutshuling(4hrs).
Take a taxi from taxistand to thimpu( 5 hrs) and halt overnight.
(Norzim lam - main road in thimpu with hotels).