Strange that you see tours paired with Bangladesh, I am not aware that Drukair or Bhutan Airlines fly direct to Paro from there. We flew in from Kolkata to Paro in a Drukair ATR42 and out to Dehli on a Bhutan Airlines A319. Bhutan tend to do a circular Dehli-Katmandu-Paro which does mean on a good day you are guaranteed to see Everest.
Katmandhu gives you the advantage of becoming acclimatised with the altitude, Paro and Thimphu are already 2000m, Delhi is a blast furnace. Kolkata is brilliantly bonkers.
2 companies I know of who do tours and organise your a) e-visas and b) flights to Paro are Intrepid and Langur Eco Travels. Not aware that there are trips specifically for Photography, but our trip was done with Langur, a birding company, who were aware that a) we were photographers b) not hell bent on getting numbers/lifers c) wanted to experience culture ie homestays and festivals/monestarys and tailored our trip accordingly.
2 things to say: $100 per person per day 'sustainability fee' - this goes to infrastructure - roads and healthcare. We need to visit a hospital - no charge. Roads are better than you believe. The Bhutan/Drukair flights are not cheap either. Everything else is unexpensive. Hope that that has sold it to you James.
I am only just making a start with my images after 10 days of my PC pretending to be the 'Orange Thing', and youtube tutorials on fixing MS Win 11 errors a total waste of my time...pleased with my bird images so far, but the ones with the people resonate a good deal more.