I've put together a list of some of the best bluebell woods (that I've visited) in North Yorkshire.
Newton Wood & Cliff Ridge Wood, Roseberry Topping
The woods surrounding Roseberry Topping are number one on my list. During May, the woods are carpeted by purple flowers, with the bluebells at their peak around the middle of the month.
Beningbrough Hall
Beningbrough Hall is a large Georgian mansion near the village of Beningbrough. The hall is owned by the National Trust, however, you don't need a membership to access the bluebell wood.
Hackfall Wood, Grewelthorpe
Covering 120 acres, Hackfall is home to a bluebell wood as well as four listed buildings. You can walk to Hackfall from the nearby village, Grewelthorpe.
Doctor's Wood, Grosmont
I only found this bluebell wood recently, just a short walk from Grosmont Station. There were lots of bluebells to see, although they were outdone by the swathes of wild garlic, which was in full bloom.