Do you actually mean 'road' or is it somewhere to ride where you and your bikes/you won't get covered in cack?
If you head through Durham towards Nevilles Cross you can access the cycle routes which can take you in several directions eg. towards Brandon or the other way towards Lanchester but if it's only an hour on the road you would be as well looping around Durham. You could try the following
Head in to Durham, over the river and right towards the hospital, through Framwellgate Moor, A167 to Plawsworth, at roundabout take a left to Sacriston, Witton Gilbert, Langley Park where you can join the Sustrans route which will take you straight back to Bear Park then Durham. Or you can hang a left at Sacriston or Witton Gilbert which will take you straight back to Durham by road.