I just got back from Bhutan 3 days ago. I was also having the same doubt as you.
From my experience my ICICI bank debit card did work at the shops and hotel. I could also withdraw Ngultrum (bhutanese currency) from bank of bhutan's atm. But to be on the safer side you should carry some cash with you. Indian Rupee works fine (100 currency and less) everywhere in Bhutan.