Cycle Racks & Routes
Woodstock can be the base for cycling in the Cotswolds, for example see this web site:
Routes in the Oxfordshire Cotswolds
The National Cycle Network web site has routes through Woodstock.
Some commuters to Oxford, prefer to cycle and the city provides dedicated cycle routes, for example see
the web site: Cycling and Walking in Oxford City
There are places to "park" your cycle just by the Town Hall.
These signs can be seen in or near Woodstock.