So since you have to basically go on a tour (unless you volunteer), it’s fairly easy to get a visa – see The Bhutan Visa Myth. Book a tour and they’ll sort the visa for you. Another example on onestep4ward.com.
Volunteering is certainly possible, and a quick google reveals many who have done it. I’ll try and indicate different examples, as each might be harder or easier for future readers.
A family who volunteered through Health Volunteers Overseas.
Several posts on UN Volunteers from people who have done it – including a page on How to volunteer.
Another blog post on volunteering there describes volunteers from Japan, Singapore and New Zealand.
Finally occasionally OneWorld365 has volunteer positions advertised.
Many other such sites would exist as well, google certainly showed many more. What’s important, however, as the last blog post pointed out is that you should only volunteer to actually contribute something towards their country, not just to avoid a tourist fee. Of course, if you can succeed in doing both, everyone wins!
Credit:stackoverflow.com‘