Whenever you are in transit in any airport, you don’t need a visa, so long as you are checked all the way through. If your luggage is checked to the final destination, then you won’t require a visa in transit.
However when you are connecting to Bhutan, this is not the case. Your international flight arriving into Delhi or other airports in India, in most case or almost always cannot transfer you luggage to the final destination into Paro, Bhutan.
In Delhi, the solution to this is to book Eaton airport hotel. They claim your luggage, bring it to the hotel room, and later when it is time for you to depart, they will check-in for you as well and bring you the boarding pass for flight to Bhutan.
If you leaving Bhutan and you are in transit in India, in most cases, the airlines from Bhutan, i.e Druk Air and Bhutan Airlines are generally able to check you luggage all the way through. You have to request them at the time of check-in, stating that you do not have Indian visa. These airlines have ground handling staffs at the airports in India and they will help get to the airlines that is taking you to the final destination.
If you booked Eaton Smart – Transit hotel in New Delhi international airport, on your way to Bhutan, and you don’t have Indian visa or you don’t want to go out into Delhi, and now you are wondering how your baggage is handled and how your boarding card and wondering how your baggage is claimed, , upon disembarking from the plane, look for Eaton hotel counter, or their staff. They will take or direct you to the hotel. Do not go through Immigration. Easton hotel will claim your luggage and bring it to your room. They will assist you further if you need to check in to another flight. You can read more about it on https://faq.windhorsetours.com/questions/question/transist-hotel-in-new-delhi