Taxi ride to Shanghai will be expensive, if it's late at night, price will go up even more. There is a shuttle bus to Shanghai which waits on the AirAsia X passengers from KL (ticket counter beside airport exit #6), you can try that.
Shuttle bus will take 3.5 hours to Shanghai and drop you off near the Metro Line 4, NanPu Bridge station. Once you get off, try to flag down a taxi by the road to get you to Ningbo road. Taxi in Shanghai is very well regulated and can be flagged down almost anywhere in the city 24 hours a day. Taxi ride to Ningbo Road near People's Square, without traffic should be ~20 mins. Just ignore the touts at the station.
Otherwise, spending a nite in Hangzhou is not a bad idea since you are arriving so late, try homeinns.com for clean and affordable accommodation.

Yes, Mr, WeiTuck is right. Another tips, you could purchase the bus ticket in advance on the plane to ensure a seat. And, the fare is a little cheaper.