I bike through Bluebell woods in Bentley everyday on my way to Manningtree which is quite nice but not that big.
There are some nice rides around Foxhall stadium.
Thomas Cycle revolution ride out at 6PM every Wednesday. I'm sure they'd be happy for another person to join.
Friday Woods in Colchester is good and bigger than you'd expect, crossing Mersea Road and leading to Donylands as well. Check the map.
Basically, get yourself lost and see where you end up that's what I do!
Also there are local bike races.
Try this:
http://mudsweatgears.sxevents.co.uk/
2nd series race is in Thetford Sunday 8th
And this:
http://www.thetfordmtbracing.com/
Hope this helps.