The inter-city bus between Hangzhou and zhoushan islands will begin operate this 30th. You can take one of those buses either at Hangzhou South Bus Station or the Hangzhou Passenger Transport Central Station. Then change to a ferry to Putuoshan. The bus ticket fare is rmb70 per one.
FYI: Transportation Between Hangzhou and Nearby Cities(https://www.travelchinaguide.com/cityguides/zhejiang/hangzhou/transport-nearby-cities.htm)

Oh..when is the best time to go there?
If I go by bus, how long to go there?
If I go by ferry, how long to go there?
Do anyone know which is the good hotel to stay there?

Thank you very much.