For a moment, put aside the emotions and try to have a rational discussion.
If Bhutan is neutral, then it is quite expected out of a country which is not at all a match at the political level and in other level to even argue or fight with China for its territory. China is a military power and China is using its power to victimize smaller countries like Bhutan. So definitely, they are worried as they may not trust completely with India,not because, they do not like us, rather it is due to the global stature of China and its veto power in UN council.
So Bhutan may not want to be a reason for war between 2 nuclear powers. The next questions is what is China going to achive by threating such small nations? Honestly, even i am surprised, why China is behind Bhutan?...Fighting with India or border issues, makes sense for me...But even they do not leave such small countries to remain in peace with their desire to make every one to listen and obey the Chines narrative of the world.