The cheapest way should be taking train from Shanghai to Ningbo. However, there are only 8 trains leaving for Ningbo and take over 4 hours. So, going to Ningbo by bus is suggested.

Will you arrive at Shanghai Pudong Airport? If yes, you could take the airport shuttle Line7 to its terminus-Shanghai South Railway Station. It takes 20yuan and 30~40 minutes. The Shanghai South Bus Station is also located here, where you could catch a bus to Ningbo with a fare of 99yuan. It will take you about 2.5 hours.