hi, there is **** all that is legal. HOWEVER, if you would like to push your bike along a footpath…
bike to falling foss (once in the woods its decent, takes about 30mins), drive to dalby, drive to the woods near guisborough(good fof DH). There is a good loop between Goathland- Beck Hole- Grosmont- Egton- Rosedale and back… But it's all footpaths and littered with walkers, but some of the best 'pushing' i've had outside of the peaks…
the railway track to RHB is tedious, best avoided unless the aim to go to the many pubs there. The railway track north of sandsends to Runswick Bay is worth doing. You can visit 'the moon' and 'the tunnels' if you do some exploring…