I came back from. Bhutan last month. You won't find any flights on normal booking sites.Bhutan have two airlines. I suggest you check druk airlines online and go to there site to book tickets. But it will surely turn out to be much costly. And yes none of Bhutan flights starts from Mumbai. Either you have to get to Delhi or kolkata. The budget option is to take a flight to Bagdogra and then go by road which has turned out to be cheap for me