According to the Routeing Guide and NRE Journey planner, Bristol to Walton on Thames is NOT valid via Shepperton, but then I'd be surprised if anything other than Shepperton is valid via Shepperton, being that it is at the end of a branch line!
Your other hope would be that the two are
Interavailable origins and destinations. They are not.
So what is to be done?
Well one solution would be to find the nearest common stations to where your ticket is valid and then purchase a separate ticket to allow onward travel to Shepperton. This would appear to be New Malden if going via London. Please note that if you use this as your splitting point the train must stop at New Malden. An off peak day single from New Malden costs £5.90, assuming you are an adult with no railcards.
EDIT: I've just realised New Malden is also being bustituted... back to the drawing board!
FURTHER EDIT: Clapham Junction appears to be the closest to Shepperton you can get going via London on a ticket from Bristol to Walton on Thames, whilst avoiding rail replacement buses. It's £7.60 for a single, again assuming you are an adult with no railcards. Advice about the train needing to stop there still applies.
A better option might be to avoid London. It is worth noting that there are no 'via London' tickets and the only return tickets valid from Bristol to Walton on Thames via London are '+Any Permitted'. You would be permitted to avoid London and take another permitted route, which may get you closer. Can you confirm to me exactly what sort of ticket you hold? I was thinking something along the lines of going via Kingston, not via London, and buying a single from Kingston to Shepperton.... though the complexity of the routeing guide combined with the time of night and the diversions (particularly as they involve a doubleback) is making my head hurt a little! May have to leave this to others for now!