A search for "Drove Roads" may find you some.Copied from the article:
"Welsh mountain ponies were traditionally used to transport goods to market, plough fields and work as pit ponies in the mines, not for riding. Their once widespread use is the reason thousands of miles of bridleways were cleaved across the countryside, creating a network of rights of way that exist to this day."
Is that true? Is there a map of the old ways?
As SarahR said "Must be, somewhere. You can see current bridleways on the OS maps though and they are very common, although not necessarily linking up in any meaningful way.".
I believe that some of the old Drove Roads still exist, not necessarily as bridleways but as paths and tracks, on the Open Country areas, etc. that we still have access to under the CRoW Act. Of course, some of the Drove Roads will have been surfaced as regular roads.
I'm also aware that many County Councils provide on-line access to (a version of) their definitive maps. You could use these maps to help identify routes before shelling out for the necessary paper map(s). Also browsing the open access areas using the satellite view in Google maps will help you spot tracks and paths that are not on regular maps. If you have Google Earth installed you can do this in 3D.