According to a rough sampling exercise that I conducted, there are currently around 3,000 to 4,000 Bhutanese Twitter accounts. Abi Narayan (Twitter handle: @abixalmon) opened one of the first (if not the first) Twitter account in Bhutan: Abi's account was created on March 18, 2007, more than five years ago.
The number of accounts crossed 100 sometime in 2009, and 1000 accounts were available at the end of 2010. The rate of joining Twitter accelerated dramatically in mid-2011.
Check out the chart below (it might take a few seconds to load, so be patient!).