from the websitre:
Western half of The Ridgeway
The western half of the Trail, from Overton Hill to Streatley on the River Thames, is a marvellous route for mountain bikers (those using touring bikes might struggle a bit) and horse riders. It provides an almost continuous 43 miles (69km) stretch of track with only a few short sections of road. Some sections have a hard stone surface whereas the rest is a natural surface, in places with some damage from excessive use – maintenance to repair these is ongoing
East of the River Thames
A considerable length of The Ridgeway east of the River Thames is public footpath which cannot be used by cyclists, horse riders or carriage drivers. However there is a lovely 9 miles (14km) stretch through The Chilterns that can be used on a bike or horseback. This is from Britwell Hill just west of Watlington to Bledlow, west of Princes Risborough. Carriage drivers can use the 5-mile (8km) restricted byway stretch from Britwell Hill to the A40.
Those cyclists and horse riders wanting a long distance ride east of the Thames that uses The Ridgeway as much as possible have two good routes to follow. The Swans Way (phone 01296 382171 for leaflet) starts from Goring-on-Thames, just across the river from Streatley, and travels to Bledlow where it turns north away from the line of The Ridgeway. At Bledlow cyclists and horse riders can then join the Icknield Way Riders’ Route that provides a good alternative route to The Ridgeway as far as Pitstone Hill, just a couple of miles from Ivinghoe Beacon. Unfortunately riders and cyclists can’t continue to the end of The Ridgeway as the route to it is a public footpath.
so the west of the river you’re all good, east of it you can find a way but your route won’t be on the ridgeway itself. Sustrans do a map of it: http://www.sustransshop.co.uk/products/5292-ridgeway