According to What are the visa (or any other crucial) requirements of Bhutan for tourists? and a dozen other web pages, tourists are only allowed in Bhutan as part of a US$200 (or more) organized tour, which includes lodging and meals.  I haven't been able to find anything that says different.

So are the 111 AirBNB sites in the country only for locals?  102 of them are less than a hundred US dollars per night.