Wells to Salisbury-
The easiest way is the hourly bus from Wells to Bath (as you know the bus station is next to the rail station at Bath) then train to Salisbury.
Or you could take the bus #271/272/273 every hour from Bath to Devizes, then the bus 2/2A/X2 every hour to Salisbury (some of those route via Stonehenge).
Another more scenic route is to take the hourly bus 376 (the continuation of one of the buses from Bristol) from Wells to Yeovil for the train to Salisbury.
Every 2 hours there is a bus CR5 on the gorgeous countryside run to Dorchester South station for main line trains to Winchester.
But if you get your timings right you can change off the bus CR5 at Blandford onto the 20 to Salisbury a few times a day.
Blandford is one of those nice little towns to spend the night in. And from Dorchester you could have a side trip around Dorset.
From Salisbury to Winchester take a train, changing at Southampton or Basingstoke, or there is a very good bus service-
Bus 8 every 20 minutes to Andover, then bus 75 hourly to Winchester; or at 0730 and 1000 on a schoolday Bus 68 runs direct from Salisbury to Winchester.
It is also possible to take a train to Romsey, visit Romsey Abbey then bus 66 every 30 minutes to Winchester; every 2 hours bus X7R does Salisbury to Romsey
Many permutations.
For Bourton on the Water to Wells the most obvious route is the bus 801 every hour to Cheltenham Spa, train to Bristol Temple Meads, then the bus every 30 minutes from the bottom of the Station Approach Road to Wells.
From Cheltenham to Gloucester there is a very frequent bus service- so either would make a good intermediate base. And trains also run frequently from Gloucester to Bristol. The interchange bus to train is much easier at Gloucester than at Cheltenham Spa.
You can actually very easily (if slowly) in a day go from Winchester to Heathrow by local buses via two different routes for a £10 note but that is a different story- a route I am scheduled to do (starting in Salisbury) in just over a week's time.
