Central Bedfordshire Council's countryside access team have designed some nice self-guided walks, most of which are circular and stile-free. You can print out directions and maps.
Local self-guided walks include:
The Greensand Ridge walk is a long-distance walk of 40 miles (64 km) that crosses Bedfordshire, with brief sections in Cambridgeshire and Buckinghamshire. From its southern endpoint at Leighton Buzzard the route runs north-west to Gamlingay, following the Greensand Ridge, a distinctive feature that rises from surrounding clay vales to give a landscape of gently rolling hills and small valleys, often heavily wooded and rich in wildlife.
The Biggleswade Green Wheel was launched in 2015. It is fully open to walkers, and over 90% can also be used by cyclists.
The Sandy Green Wheel walking route was launched in September 2018. Central Bedfordshire Council are currently working with landowners to create additional sections to make them suitable for cycling.
The Etonbury Green Wheel will be launched in two stages - a walking route in 2019, followed by the full cycling route when possible.
There is a full list of walks on the Central Bedfordshire Council website.
Lets Go is a great website with lots of walking resources.
Walking in England also has a number of walks listed for the Bedfordshire region.