I grew up in Bangladesh. Not far from Bhutan. My family used to go there all the time. Not in Airplane. It was a bus ride to the the India/Bhutan border and it was more like hike. That was long time ago of course. Now Drunk air flies from Dhaka Bangladesh to Thimpu so my family flies them. I left home 7 years ago, so not sure how it's like now, but when I left they had a wried route where they flew everyday from Bangkok, to Dhaka to Thimpu and back to Bangkok. I think they based airplanes at Bangkok. So to come back to Dhaka you had to fly via Bangkok. This travel agent that used to sell me airplane posters (very hard to find in bangladesh) told me one leaving their airplane at Bangkok was necessary to keep machines out of there in the evening to stay in natural world. Could be complete bs or could be true. That travel agent talked a lot of bs. I never complained cause she brought me big airline posters.
Well I don't know much about Bhutan, but from what I do know is that it's almost a miracle that Bhutanese even allowed flying airplanes in their holy land. Of course I'm not future teller, but I'd say the chances of Bhutan allowing others to fly in there is zero. I don't think they are really concerned about establishing any instrument stuff. Less flights is only good for them cause they can have more peace.
I can't live the kind of life style they live, but they are happy that way good for them. So anyways back to the topic I'm sure if the route looks busy many airlines would jump in. Many westerners these days dream of going there. I think Angelina Jolie goes there too. So if their sky is open there no telling how many airline would wanna go there, but I don't think Bhutan would allow that any time soon.
I'm assuming you are staying in Bhutan now. It's a great place to visit, but a little to isolated and peacefull for me. If I get stuck there more than couple days I think I'll go insane.