There are five buses leaving from Shanghai South Bus Station to Haining everyday, and takes about 2 hours on the way. But, only one bus from Haining to Zhuji and no train. So, I'm afraid that you have to transfer at Hangzhou. Firstly, you could catch a bus from Haining to Hangzhou East Bus Station or Hangzhou Coach Terminal (1.5 hours). Then, please go to Hangzhou South Bus Station which supplies frequent buses to Zhuyi(1.5 hours).