Exploring Oxfordshire by bus is an experience you will miss if you stay wedded to your car. For keen walkers, it is a journey to freedom, because you can finish when you get tired and you do not have to return to the dreary car park where you started.

But if you have not climbed on board a bus since your schooldays, it can be difficult to work out where to go and what to do.

So I am starting this series with one of the easiest routes.

Bus operator Stagecoach has imaginatively named the Oxford to Swindon bus ‘Route 66’ (a clever reference to the iconic highway in the United States). I would be the first to agree that Swindon Bus Station is a pretty grim place, having spent unhappy half-hours there waiting for the National Express bus to escape to Cirencester. But Route 66 does takes you through some interesting countryside.

It leaves Gloucester Green at15 and 45 minutes past every half-hour, or hourly on Sundays. You might expect it to stop in Cumnor, but in fact you speed straight past on the A420, so if you want to see what Matthew Arnold described as “the strippling Thames at Bablockhythe” you would need to catch a City4.

Route 66's first useful stop for walkers is The Greyhound at Besselsleigh. For those whose bus etiquette is rusty, it is OK to tell the driver you are a stranger and to ask him or her to let you off there — rural bus drivers are generally quite friendly,.

A walk from Besselsleigh could stretch from two miles to seven or eight, depending on stamina. You need the Ordnance Survey map 180 (Oxford) or Landranger 164. For a two-mile walk to Appleton, cross the A420 and walk down the lane to the hamlet of Besselsleigh, with its picture-postcard thatched cottages. The map, and some transport websites, spell the name as Bessels Leigh, but locals seem to spell it as one word.

Dilettantes may wish first to have coffee in The Greyhound, open from 11.30am (noon on Sunday). The 19th century innkeeper here was Alfred White, who also ran a bakery, shop and forge where he recast church bells. Whites of Appleton is now the oldest continuously trading bellhanging company in the UK.

Take a footpath left to Besselsleigh Community Wood, keeping straight on to Appleton Church with its Norman windows and canopied table-tomb dedicated to Sir John Fettiplace. As you would expect, it has a keen bell-ringing team. The village pub, the Plough, is open every day from noon, but does not serve food on Monday lunchtime(call 01865 863535).

Retrace your steps, taking a right fork in the wood through Besselsleigh estate until you reach the A420. From here, you can walk back towards the Bessels Leigh School stop to catch the bus back to Oxford.

Alternatively, you can extend the walk for another five miles by crossing the road and walking down Rowleigh Lane to take a footpath left to Dry Sandford.

Walk north through Wootton, taking a bridleway on the right to arrive at the Bystander Inn crossroads. Cross to take the road to Wootton village, taking a right turn just past the church signposted ‘Old Boars Hill’.

A footpath on the left takes you up the hill, with a wide views of the Chilterns and Didcot power station. The path eventually rejoins the road at Jarn Mound, built by the archaeologist Sir Arthur Evans. There are no ‘magnificent vistas’ from Jarn Mound these days, because trees now block the view.

There are, however, views from Matthew Arnold Field, owned by the Oxford Preservation Trust. Arnold’s poems The Scholar Gipsy and Thyrsis are said to have been inspired by this view stretching across to the Downs, and his Victorian poetry reflects his belief that landscape and the natural world could be a remedy for “the strange disease of modern life”.

Three paths lead from this corner. To return to Besselsleigh, follow the central one leading diagonally across the field through woodland and then to the left of Youlbury Scout Camp to join the Henwood bridleway. If you turn left here, this long track takes you back to Besselsleigh, while to the right it leads to Westminster College, where a Brookes bus would take you to the city centre.

For a three- to four-mile walk taking in the best views of “that sweet city with her dreaming spires” mentioned in Arnold’s poem Thyrsis, leave Matthew Arnold field on the right-hand path next to the fence, then find a footpath leading between two gardens to Chilswell Farm, walking through the ‘happy valley’ nature reserve to reach the Oxford ring road. Continuing in the same direction over the flyover and through South Hinksey village brings you to the Devil's Backbone, a historic raised pathway across the water meadows. You end up in Hinksey Park, where there are frequent buses to the city centre.

However, if you want just one day out on Route 66, it has to be Faringdon. Get off in the Market Place (the bus should stop here for a few minutes, so there’s plenty of time). Incidentally, the 17th-century market hall might suggest a wide array of tea shops, but after 5.30pm and on Sundays there is very little open.

The main attraction here is Faringdon Folly. Built in 1935 by Lord Berners, the then owner of Faringdon House, for his young friend Robert Heber Percy, it is a monument to British eccentricity, and has some of the best views in Oxfordshire. The last folly to be built in England, it is open on the first Sunday and bank holidays. Even if the folly is closed, the views are breathtaking. The view from the folly is described in detail on the website www.faringdonfolly.org.

Walk towards the church and along Church Street. At the end of the churchyard there are the old gatehouses belonging to the original Faringdon House, and Faringdon House can be seen through a hole in the north wall. The large stone house opposite was the original vicarage, now converted to flats.

Follow this road until it becomes a footpath, with magnificent views of the Thames Valley opening up to the left.

You can see the folly on your right, and the route, which is waymarked as an Oxfordshire County Council circular walk, takes two right turns, the first being just past Grove Lodge, a house with a large Skyflash missile in the garden.

It dates from 1978 and is a medium-range air-to-air missile. It was deployed by a Tornado in the 1990-91 Desert Storm operation. By way of explanation the owner of Grove Lodge, Ian Smith, an aircraft enthusiast, explained: “A friend asked me if I would like to buy a rocket.” So he did!

Ian also owns Venn Mill near Wantage.

The Cotswold ridge stretches to Rissington, and below is Thames Valley, from the source beyond Lechlade to Brize Norton airfield and Shipton-on-Cherwell cement works, then Boars Hill. On the other side are the Chilterns and the Berkshire Downs. Uffington White Horse can just be seen as a squiggle on the ground.

Walking straight down to the town, another circular walk is available to Badbury Hill, a National Trust wood famous for bluebells, where there is a satisfying view back to the folly. The route passes the 13th-century tithe barn at Great Coxwell, with its original timber beams.

We skipped the final part of the circular route and walked on a tarmac path from Coxwell to Faringdon Golf Course, and a welcome bus stop bearing the number 66.

n The Faringdon circular walks are waymarked and described in Oxfordshire County Council leaflets and at www.oxfordshire.gov.uk/walksandrides Faringdon Folly is open on August 7 and 29. (www.faringdonfolly.org.uk). Contributions and comments appreciated on my website www.groundhogwalking.co.uk