When you arrive at Pudong Airport, please take the shuttle bus Line 7 to Shanghai SOuth Railway Station. On its south square, you will find the Shanghai South Bus Station, which supplies buses to Zhoushan Putuo Bus Station directly. The last bus will leave at 19:10, so you could catch one easily.

Hello Mr. Jams and thanks so much for your fast reply!
I was researching possible ways and was thinking to take a bus ZhangJiaGang - Ningbo South Bus St. and than get to Zhoushan from there. So, do you suggest going through Hangzhou is faster?