Hi, tawoh.
Which route are you planning to use to return from Carn an Righ to Spittal of Glenshee? The walkhighlands route...
http://www.walkhighlands.co.uk/perthshire/glas-tulaichean.shtml...is circular from Dalmunzie Hotel, so the only bit where a bike would be of use is getting to that hotel from the Spittal, which involves only about 2km along the driveway. Some walkers park at the Dalmunzie Hotel anyway, so a bike would only be useful if you were returning along Glen Lochsie with an out and back route, rather than via Gleann Taitneach. On the map, the most feasible out and back route looks to be back over Glas Tulaichean. Apologies if you're already thinking of doing something like that anyway.