De·ci·pher - ing the UKs Rural Bus Transport System

Ticketing wise all local buses in England cost no more than £3 a ride (in some areas less) as a fare cap.

In Oxfordshire there is an all operators Day Ticket called My Bus for £6.50 a day which will usually be your best option- https://www.mybusoxfordshire.org.uk/mybus-oxfordshire-tickets

That website links to the websites of all individual operators - from which full timetables can be downloaded. The primary operators in the area are Pulhams and Stagecoach West.

Google maps is your friend in this case- blow it up and it shows you where bus stops are, and a full list of departures from each stop.

Traveline will also help you plan journeys.- https://www.traveline.info/

Oxfordshire County Council does not appear to have a county wide bus map on it's website.

After some to-ing and fro-ing on the bus times website (and offline data) Kelmscott has no bus service that I can trace. It is a taxi from Lechlade.

Burford only has two useable services- the S2 every two hours from Oxford to Cheltenham calling into Witney (run by Stagecoach), and the Stagecoach hourly 234 local bus from Burford to Witney. The 1007 service on that route provides a good connection into the 64 at Witney. Witney is actually a good centre for buses including one a day to and from London of all places.
Other routes from Burford are either once daily school buses or village shopping buses.

The only useable service to Lechlade is the infrequent 64 from Witney run by Pulhams (bound for Swindon). On a Schoolday only there is a bus 77 run by Stagecoach West from Lechlade at 1657 direct to Burford, arriving at 1725. That is a double decker, as it is a school bus that started in Cirencester.

In summary a degree of detective work is needed, there isn't a simple answer.

Burford is a beautiful town and I like it very much but I have only visited (many times as family lived nearby) by car. The lowest part of the town is where the road to both Stow on the Wold and Chipping Norton crosses the river near the church. The road then climbs up to the A40 trunk road which runs between Cheltenham and Oxford. That hill up from the river climbs gently at first but by the time the shops have run out up to the school and A40 it is quite steep indeed. I have seen people driving fail to make it up who have to stop and try again.

I would have thought that Burford would be better suited for having a car than relying on buses. As I think about it I have never actually seen a bus in Burford.

For that general area Stow on the Wold is a good hub for what buses are available, maybe Bourton on the Water if you go out to the main road for the Cheltenham/Stow on the Wold/Moreton in the Marsh buses.

Thank you isn31c and Nigel for your suggestions. Since I haven't been in the UK for many years, I have to rely upon the comments of others and suggestions made by the companys I have relationships with. The private garden tour staff made the Burford referral as an attractuve place to stay near Kelmscott. Since driving in the UK is no longer on the map for me, I have to rely upon public transport or the occassional car for hire. I will study the suggestions given and see what might be possible. Thank you, again!

Another thought- from Lechlade Bridge it is a 3.7 mile (1 hour) walk to Kelmscott on the Thames Path beside the river. That path continues all the way into London- in a further 144 miles time you reach the Tower of London! or just 26 miles to Oxford.