Head out of York following signs to first Huntington, and then towards Strensal. Pickup the road which runs along the edge of Strensal Common, before crossing the railway at the gated crossing and following a rough tarmac then gravel track. Hybrid bikes should have no problem with this, but road bikes with skinny tyres may be better off carrying on around the roads near by, via Flaxton.
Follow the minor road up to Thornton le Clay, and then to Foston, and finally to the A64 by Barton Hill. Take care crossing the A 64 as the road here is very fast. Head along minor roads sign posted for Barton le Willows, and then follow the signs to Howsham. At the bridge stop. A side trip (you can walk the bikes along the footpath) to see the mill at Howsham, which is being restored to generate hydro power is a worthwhile break. See the website for more details and open days etc. To get to the mill, turn left into the carparking area and walk under the bridge, the mill is 1/4 of a mile along the river bank in the woods.
From the bridge head back the way you came, and turn left, which is sign posted for Harton. The woodland on the right is open to the public and makes a pleasant rest spot. At the next junction turn left towards Bossal, and at Bossal follow signs for Sand Hutton, just before the village you'll pass a war memorial at a junction. At second left in the village follow the the signs to Upper Helmsley and climb the gentle hill to the village.
From the village descend until you reach a junction just after crossing a bridge over an old railway. Turn right up the hill, and then head downhill towards Warthill, and then turn right, following sign to Stockton on the Forest. Turn left and go into Stockton on the Forest, a long ribbon type village. Cross the A64 via the bridge and head into York on a residential street, through Heworth until you arrive at a road about. Head toward York centre, and soon you find yourself at Monk Bar.