No minimum number of people are required. Better to plan your own trip. Bhutan is a easy to travel country. I will suggest you hire a car . It will be more convenient . You can get down on your way anywhere you want to click pics or take a break
Knowing about the Vajrayana sect of Buddhism is an important thing to do when vising Bhutan specially Thimpu.It is an early accessible country where you can travel freely in group or solo.
I would suggest to go for a customized package. By this you will have every thing sorted out and at the same time enjoy more and as per your convenience.