There is a train leaving 17:04 to Wuhan daily arriving 16:31 next day passing Mount Wuyi at 05:49.
The new Fuzhou - Xiamen High Speed train stops at Quanzhou which means Quanzhou is connected to Shanghai by train via Fuzhou.
Bus to Fuzhou leaves from the bus station at the southern end of the main tourist street not the main bus station and takes about 3 hours ¥60-70. There are also Fuzhou busses from the small station next to the Overseas Chinese Hotel.
Several times a week, there is an early-morning bus to Mount Wuyi and Jingdezhen. This bus is small dirty sleepers, arrives at many of its destinations very late at night, and drops passengers off by the side of the highway rather than the bus station. So book with care.
There are two long-distance bus stations in Quanzhou, so make sure to book the correct one.
Chongwu is an old walled town near Quanzhou. There are good beaches near it.