the campsite between Holford and Kilve is pretty good, not too far from trails/pub either. go along the A39 through Holford, and where there’s a sharp LH bend, the campsite is on the right. i’ll be there myself in fact!
i also stayed in a little campsite in Currypool Mills once, which is nearer to bridgwater. it’s a much longer to ride to the hills though. also they have some strange water features which trickle all night – not good if you’ve got a full bladder!
as for trails, the main big walking trail which runs the length of the hills (macmillan’s way i think?) has some fun sections. from there you can dive down into any of the combes and ride back up
anyone know if Stella’s tea rooms is going to be open? last time i was there it looked very closed