If you're happy to use Advance tickets, the journey can be made for £42.60.
There's currently a Southern only Advance available from Three Bridges to Leighton Buzzard on Monday, departing at 11:34 and arriving at 13:47 (changing at Clapham Junction), for £8.50.
And there's Advances available for £34.10 from Leighton Buzzard to Bristol Temple Meads on virtually all services to via Bath. Note - there are no direct Paddington-TM trains due to engineering works; you need to change for a bus at Bath or Bristol Parkway, but the former route gives much better Advance availability.
Now it's worth noting that the outward journey above involves using the Southern service from Clapham Junction to Milton Keynes, which is suspended under Southern's "pingdemic" timetable. But
Southern has arranged ticket acceptance (not that there'd be much alternative in this situation!) allowing you to travel on the Victoria line from Victoria to Euston, thence on WMT, so whilst your journey may take a little longer than planned, and you'll have to change once extra, you won't have to pay anything on top:
The following ticket acceptance is in place on weekdays:
London Northwestern services between:
- Milton Keynes Central and London Euston, for tickets routed via the West London line or Southern Only
London Overground services between:
- Watford Junction and London Euston, for tickets routed via the West London line or Southern Only
- Clapham Junction and Willesden Junction, for tickets routed Southern Only
London Underground services between:
- Victoria and Euston on the Victoria Line
It will cost you rather more than £8.50 for Three Bridges-Leighton Buzzard if you buy a ticket after Saturday, as the "pingdemic" timetable appears on journey planners on Sunday for each following week - therefore you wouldn't be able to buy a Southern only Advance.
If you want to use walkup tickets, your best bet will likely be to get a Thameslink only Off-Peak Day Travelcard (£17.70) plus an Off-Peak Day Return from Boundary Zone 6/Hatch End to Leighton Buzzard (£15) and a Super Off-Peak Single from West Drayton to Bristol TM (£36.20 route not via London). That would add up to £68.90, but the latter ticket would restrict you to services departing Paddington after 7pm, which means you couldn't get to Bristol before 21:05.
Alternatively you could avail of the above Southern ticket acceptance, and replace the first two tickets with an Off-Peak Day Return from Three Bridges to Leighton Buzzard (£32.20 route via Kensington Olympia), albeit you'd have to pay an extra £2.40 for Oyster/contactless PAYG on the Tube (as ticket acceptance only applies between Euston and Victoria, not Euston and Paddington). That would add up to £70.80.
If you're making any sort of return journey within a month, it may be cheaper to get different tickets, so I've written the above on the assumption it's a one-way journey.