At the Shanghai Passenger Transport Terminal, there are about 10 buses departing to Liushi directly from 08:30 to 23:00 everyday. The bus fare is about 180RMB per person and takes 5.5 hours one the way,

Take a bus from Shanghai Long-distance bus station. The price is about 180 yuan. The earliest one is 8:30.

I will make the same journey and will use the Bullet Train

I'm afraid there is no direct train service between, let alone bullet train and the bus should be the best way.

As a second choice, you can go to Shanghai Hongqiao Train Station to catch a bullet train to Wenzhou South first. Then transfer to another bus from Wenzhou to Liushi.