Last August, as I mountain-biked down 10,302-foot Dochula Mountain Pass, just outside the capital, Bhutan’s eldest prince zipped by me on a b’Twin racing bike. Soon after, the prince’s elder brother, the Dragon King, passed me with his 30-person entourage. Both men stopped to chat. Which is to say, don’t miss Dochula, a 25-mile descent through blue pine and rhododendron forests that ends in front of the Chimi Lhakhang monastery. Budget an extra $20–$50 per day for a Kona hardtail and support vehicle from Guides of Bhutan. Other can’t-miss rides: the northwestern singletrack route across a 500-foot suspension bridge in Punakha, and the central Bumthang and Ura valleys, dotted with monasteries, temples, fortresses, and deep-pink buckwheat fields.