It is suggested that you take a bullet train from Shanghai South Railway Station to get to Hangzhou Railway Station firstly. And then, you could take the airport shuttle bus or a cab from Hangzhou Railway Station to the airport directly. You could search the train schedule at https://www.travelchinaguide.com/china-trains/

there are two railway stations, is there a bullet train at the main shanghai railway station?

No, all of the trains from Shanghai to Hangzhou are departed from Shanghai South Railway Station. It could be reached easily by subway Line 1 and Line 3.