It's been done, or large chunks of it have, but – in no particular order – Doctor's Gate is a Marmite sort of trail, you either like it or not, my personal opinion is that it doesn't have much flow and is a better running than biking route. A lot of William Clough – the upper section – would be very hard to ride. By Ashop Clough, I guess you mean the Snake Path, which is a lovely trail, but bear in mind that the surface tends to show bike tracks pretty clearly and the Peak Park folk get very animated about any cheeky riding around the Kinder area.
If you were, ahem, theoretically going to do it, you'd mostly likely ride up Chunal out of Glossop, cut across Middle Moor then front the top round the corner to Willam Clough – staying high, nice singletrack – push up William Clough (if you want to ride, paved slabs from the summit of Chunal up to Mill HIll are very rideable albeit dull. Down the Snake Path, wooded singletrack. Interminable ride up A57 then down Doctor's Gate into Old Glossop I think.
Good route very early on a Sunday morning but back over Cut Gate rather than Doctor's Gate if you want better riding on the return leg.