I envisions the final design on rectangular canvas with "name" "Company name" and other details mentioned in "Details to include on the business card" and not just a logo. Maybe be best to look how some of the winners on this site have designed logos and cards.
A design I love is attached below (first file). If you can get inspiration from that, then that's awesome. This is from wikipedia page on Bhutan. There are some more to kind of show the bhutanese colors and the minimalist style.
Here is more information.
I would like something that reflects/captures/incorporates the following
1.) Bhutanese drawings/fabrics
5.) A blend between 1-4 and minimalist style.
Bhutanese culture as a whole uses vivid colors (orange, yellow, red, green) with dragons. I would like this to be incorporated into the "Bhutan Teas" business name.
It is best to google something related to bhutan to get some kind of inspiration as words cannot describe it well. For example, "Bhutan fabrics and dragons" gives wide array of interesting images from where to begin.
It would be preferred if "Bhutan Teas" business name to be incorporated into the patterns and preferably contain a dragon.
Since business cards come in different sizes, but are typically rectangles, I would want this to be scalable so I'm not sure what that means to designers, maybe make it as big as you want and later I can scale it to the appropriate business card size.