To get into the nature reserve, take a minibus from Muyu to Yazikou (RMB 10). These only depart when full, so there may be a wait involved. Another way to go is to rent a bicycle from Yuanmeng Huwai Yundong Luyou (RMB 50, deposits RMB 1000), just down the road from the restaurant, and to pedal the scenic, though demanding, 14 kilometers.
Wuyu can also be reached by bus from Yichang, there are departures thrice daily at 7am, 7:30am and 2pm (RMB 50, 4.5 hours). Although Wudang Shan is not closed to foreigners, travel north through Shennongjia to get there is not permitted for foreigners.
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Shennongjia on the China Travel Blog