The best and most reliable way to process a visa (E Tourist Visa) for India is through a Government of India website https://indianvisaonline.gov.in/visa/tvoa.html. Do note that the E Tourist Visa will costs you $100. There are many fake websites pretending to be the government site but charging additional fees. This link is the most reliable.
The E Tourist Visa will give you 3 months, multiple entry and therefore, with this visa you can return back to India from Bhutan.
For those just passing through and only going into Delhi for one month, one could think of a Transit visa.
There is much confusing information on the internet and no definitive facts. Safest would be to get the visa mentioned above. Even if you are not leaving the airport, you will probably need to clear immigration in order to collect you baggage and check them in for the flight to Paro, so in this case, you will still need a visa.
You should also check with your local Indian Embassies or Consulates about transit visa possibilities, but if you are told that you can get a transit visa on arrival, you should have a WRITTEN PROOF before leaving home.
The E Tourist Visa process online is a bit messy and frustrating (Hello India!) but works in the end. Visas take up to 72 hours to clear.
This information was provided to us by our friend Martin Alyward, who is a meditation and mindfulness teacher and he visits India at least two times a year.