I spent my formative years misbehaving on a mountain bike around Norwich…
As someone above said, look North, towards Cromer, find the woodlands, the contour lines and the footpaths and bridleways and enjoy whatever you can find (suggestion…Bacton Woods…EXPLORE!)
Ringland Hills (Near Ringland Village, near Taverham)… I can remember that place when it was all virgin woodland (happy memories!)…what has happened to it over the years is nothing short of outright vandalism and so it is no surprise that mountain bikers are now decidedly persona-non-grata. Give it a go if you like but don't be surprised if you experience 'hassle' from anyone out walking their dog etc. Oh yeah… dog…there's a dogging spot somewhere up there too!
Thetford gets more than it's fair share of coverage…a bit of local knowledge goes a long way in there.
Holt Country Park seems to be mostly ignored by mountain bikers for some reason but if you're of the 'map and compass and miles of pedaling' mentality then there's probably something there for you.
Near the city centre, Mousehold Heath used to be something of a playground for mountain bikers, it's been years since I was in there but it's probably worth a look!
Basically I think the advice I'd give is that in Norfolk you're not going to get amazing trails handed to you on a plate. What you need to do is go out and explore, conduct a recce, find a good bit of trail in one area and see if you can connect it to another bit of trail in another area…
Hope that the above has been helpful and that you enjoy your time in Norwich.
PS: Suggest you try the Cherry Beer in the Belgian Monk too!