The routes may be somewhat complicated from Hangzhou to Putuoshan. You first destination should be Shenjiamen of Zhoushan City and then transfer to the ferry to Putuoshan at the Banshengdong Pier. For details:
Hangzhou to Shenjiamen: take the bus from Hangzhou East Bus Station. Everyday, there are 15 buses departing here from 06:50 to 18:50 with a ticket of 95 rmb. The journey is 5.5 hours. So, you have to set off early in the morning.
Shengjiamen to the Pier: take of city-bus of No.6 or No.7
Pier to Putuoshan: take the express ferry with a ticket of about 20rmb. The ferries operate from 05:30 to 17:30 every 10 minutes. The journey is about 12 minutes.

Well, from Putuoshan to Ningbo, you could return to Shenjiamen to take the bus to Ningbo directly. The journey is about 4 hours.