The train from Norwich to Cambridge takes about an hour and 20 minutes. It arrives at Cambridge station, which is nearly across the street from the Cambridge Botanic Garden and a shortish walk into town or frequent bus into the centre.
Where do you want to get to in Cambridge?
There is no central bus station for other than local buses, and not all buses pass through the Drummer Street area. There is no building, just a series of many bus stops. National Express don't stop there. National Express stop at a bus stop at Parkside which is near the Leisure Centre and somewhat near the Grafton Centre. They also stop at two or three of the Park-and-Rides. Again, just a bus stop, but in the case of those there is also usually a bit of cover and toilets, and then the dedicated buses into the centre. Some of the Park and Ride buses serve the Drummer Street area but others don't.
Coaches take about 2 hours, and can be delayed by all the construction on the A14 trunk road.