I wouldn't camp out in the forest, unless you like midges, I'd stay a little lower down in the valleys.
Rosedale is nice.
I would get the hard rides (on the moors) out of the way first, with a relaxed Vale of York / Thirsk/ Easingwold / Pocklington / Market Weighton / Beverley type of route to finish (tired legs)
I did a trip in May over the bank holiday. First day Driffield area, up to Malton, then Pickering finishing early at Spiers House near Cropton. Second day was a biggy, rode to Rosedale then up Chimney Bank

A nice run down to Hutton le Hole, over to KirbyMoorside, Helmsley (a horrible slog up to Sutton Bank on the A170 - no alternative really), down White Horse Bank and onto Thirsk. From Thirsk I then headed west to Masham for the night.
Day three was a long one. Set off from Masham, then went to Well, Snape, Carthorpe, Kirklington, back to Thirsk for extra brekky, then meandered down the vale of York taking in Dalton, Sessay, Brafferton, Raskelf, Easingwold, Stillington, Strensall, then over to Stamford Bridge, Pocklington before climbing up through Millington to Huggate and home (downhill 6 miles - weeeeeeeee)