As long as giant penises painted on Bhutanese homes do not destroy you, it is very safe for solo female travelers to explore Bhutan. Even multi day treks through Bhutan’s raw nature and wilderness is safe for solo female travelers. Your guide will make sure that nothing happens to you as long as you stick to the trail and don’t go wandering alone in the wild. You can also choose to opt for a female guide, not just cultural but trekking guide as well.
If you are trekking in Bhutan, you will be accompanied by a trekking crew consisting of a trekking guide, a cook and his assistant, two to three horsemen and several horses.
If you happen to be going out to check out some nightlife, I recommend you take your guide along and also check if the establishment is tourist friendly. Guides and drivers do not indulge in alcohol while on duty and I have met many solo travelers hang out with their guides at bars in Thimphu and Paro. I also know of several small and medium travel company owners who like to take their guest out for a drink or two. Having said that, be mindful of cultural differences