According to Baidu map query, you can take bus No.93 from Daimengde Hotel in Jiaxing to Jiaxing High-speed Railway South Station, take bus No.93 at Daimengde Building Station to Jiaxing South Station, take the route of 18 and get off at Jiaxing High-speed Railway South Station. The whole journey is about 12.7 km and takes about 55 minutes.
According to Baidu map query, you can also take the tram 1 line from Diamond Hotel in Jiaxing to Jiaxing South Station. Take the tram 1 at Hexing South Road Station on Zhongshan East Road to Jiaxing South Station, and get off at Jiaxing South Station after the stop 14. The whole journey takes about 1 3.7km and takes about1hour and 8 minutes.