There’s very little forest in the Peak District, so you won’t find many forestry commission/Landrover tracks (aka gravel roads).
You’ll be better off aiming for disused railway lines, green lanes and other bridleways. And obviously it’ll be worth doing some road sections to join things up. And you’ll inevitably end up doing some MTB trails, as that’s the only way to get through certain parts.
If you’re heading up from the south, you could consider starting in the southern parts of the White Peak, near Matlock Bath. Just north of Wirksworth, you’ve got the Pennine Bridleway (Midshires Way). If you keep heading on this trail, north-westerly, you’ll get through Chelmorton, and then eventually Castleton. If you then do a loop from there (I’m deliberately ignoring this bit), on the leg back, when you get back to Tideswell, rather than do the same in reverse, you can descend down to Millers Dale and follow the Monsal Trail south-easterly (disused railway line with amazing tunnels) back to Bakewell.
Have fun 🙂