You can go both by bus or train. These two cities are more than 200 km by road from each other. You can easily find buses at Shanghai South Bus Station which will arrive in Ningbo in 3.5 horus.
You can also get to Shanghai South Railway Station to catch trains to Nongbo. Ticket fare is cheaper than going by bus. Suggest you take T trains, which are faster.
Shanghai South Railway is easily reached by subway, however, buses are more than trains.