Someone I know traveled to Bhutan by road and was very impressed by the smooth roads in Bhutan. Also, he was able to see some beautiful scenery on the way to Thimpu, the capital of Bhutan. I am thinking of going by road too, instead of flying down.
There are more or less 800 miles between India and Bhutan (from near Nagpur to Thimpu) and it may take you a day or so to get there. If you think you can handle the distance, then go for it, but frequent stop overs may be in order so that you can attend to your basic necessities.
Actually the distance is the problem. I do agree that the scenery is beautiful though,but u will face issues such as. you wint find proper toilets,shops,hotels etc when ever u need them. However with friends (men) u wont fase that much problem.
India and Bhutan share a border, I don't know where you got that Nagpur bit from because that is right in the centre of India and there is no mention of Nagpur in the first post. Distance between India and Bhutan is "Zero Miles" if you stand at the border
I would also add that there are a lot of curves in the roads. As with Nepal, the terrain means the roads are seldom straight over long distances. This is great on a motorcycle if you want some spectacular views, but also means you should be a proficient driver if you want to go by car.
