Plenty of bridleways with attitude South of Cambs – even some elevation!
Try all around Wandlebury/Gogmagog Hill and also Linton. Some decent downs (and ups) the other side of Royston too. Plus, as Tommid says, you can hook up to the Icknield/Peddars Way track, and it will take you all the way up to the N Norfolk coast, or all the way down to the Dunstable Downs. Also, if you want to go further into Suffolk than Brandon/Thetford, you can have some fun in Tunstall Forest (10 mile waymarked Viking Trail is a blast) and in the forest and heath around Dunwich. Also Rendlesham Forest and XC loop around Alton Water.
So plenty if you’re prepared to be creative.