John muir way? I know a really nice circular route from edinburgh – pencaitland railway path, woodland paths to haddington, old railway to longnidry, back along the foreshore
south of Gifford there is a lot of tracks for the grouse shooting estates which are rideable but the hills are fairly steep suych as Longyester up onto lammer law and down again to stobsheil the range of hills just north of Haddington the Garelton hills is a nice path along the top of the ridge but IIRC gets a bit faint at the west end.
We don’t have bridleways in scotland 🙂