Hi, can you advise me how to get to Putong International Airport from Wuzhen?

The public transportation exists.
From WZ Bus Station, there are direct buses to reach Shanghai South Bus Station. Upon reaching the south bus station, you can walk to reach the Shanghai South Railway Station where you can take the Pudong airport shuttle bus line 7 to reach the airport directly.
The bus fare from WZ to Shanghai is around 49RMB. The fare from south railway station to airport is around 20RMB. For the whole journey to the airport on the bus, it will take about three hours. From WZ, the bus interval is around one hour and the bus to airport, the interval is around 10 to 20 minutes.