From Shanghai can I take a Taxi to Huzhou and how long does it take and cost?

My suggestion is to go to the South Bus Station to take a direct bus. The bus ride takes about 3 hrs. The buses are in operation from 06:50 to 19:28. Or You can take a high-speed train at Hongqiao Railway Station to your destination in around 2 hrs. Only two trains are in service every day, so if possible, book a ticket in advance. Taxi would need more time.