Use RidewithGPS. (It often selects NCN routes - in a good way.)
Turn on the bike paths button. Roads with green dotted lines are often great. Solid green lines need a good amount of street view investigation. Brown lines are often worth having a back-up plan for as they'll often be gross and slow if the weather isn't full summer.
Sketch out route.
Scan for anything that looks like a bigger road and drop the street view guy down to have a look. If it looks big and nasty re-route around.
Look for squiggly non-direct roads and bike paths that look like they don't follow roads. These are likely to be pretty and fun - if street view guy won't drop on them coz they're obscure and not covered, see if they have names and google fu them. Often greenways and the like will have some information online.
Avoid canals that are close to built up areas as the going will be slow and frustrating. Outside of built up areas often the riding surface will be bad or not really existent.
If you come into Bristol via Yate you can hook onto The Bramway and then the Bristol to Bath Railway Path and avoid all the nastiness of cycling into a big city.
Haven't ridden there but, Stratford-upon-Avon seems to have quite a nice run along a canal coming in from your direction and a nice looking path coming out to continue on towards Cheltenham. Stratford could be nice for a lunch stop too.
Choose hills over shitty busy roads, even if riding fixed and go the long way round every time. Enjoy being a bit lost and stop for a snack and take it all in.