As in the town of Bedford?
Ashridge, plenty of very good XC. Plenty of good climbing if you want it as it zig-zags the Chilterns/Ridgeway. Ivinghoe Beacon is the stand out area.
Woburn/Aspley woods. Hours of all year round XC. Forest and woodland, with good climbs if you want them. Also has a well used ‘play area’
Chicksands. Another old XC area with lots of man made stuff. (I haven’t been in years)
Woburn and Chicksands can be linked.
Sundon Hills. Hardly used tough XC. Best when dry. Harlington train station is a good start point.
Aston Hill. Downhill and XC course, but just a gateway into Wendover Woods.
I ride from Leighton Buzzard through Woburn and cross country to Lidlington (near the large lake and Millbrook test track) you could do that in reverse.
Many other areas can be joined.
If you race you have the Friday Night Summer Series on your doorstep.
If you fancy cyclocross we have the Central CXL.
And many of the riders I know ride and race in all sorts of disciplines. Bedfordshire has loads of great road cycling clubs and informal groups as well.