I think India handles most of Bhutan’s foreign affairs (after the Brits left they gave a lot of administrative functions of Bhutan to India). my WAG would be Bhutan’s relations with the US would go through them.
The last US State Department “Background Notes” for Bhutan was published in 1990. Under “Foreign Relations”, only a few nations had any diplomatic ties with Bhutan and only India and Bangladesh had representatives in Bhutan.
And Bhutan’s only embassy was in India.
I think it’s more a factor of logistics than anything else.