According to the Ordnance Survey Map there are no Public Bridleways in Shobden Hill Wood. Although if you look under 'Where to Ride' under Natural England there are two permissive bridleways provided under the farm conservation scheme managed by Natural England, which give access to the wood.
The Public Rights of Way Section, Amey Herefordshire, Unit 3, Thorn Business Park, Rotherwas Industrail Estate, Hereford, HR2 6JT. Tel 014432 261800 may have more information. E-mail ameyherefordshire@amey.co.uk But you need lots of patience getting through to them.