Thanks for the tips - I know a few of the routes you mention and some are new so I'll certainly explore them.
The section I'm talking about is off the main trail through Black Carr (the wide one, about as wide as single lane of a road, high above where the stream runs through the woods, the stream is down on your left if you're heading towards Bank House area) which we normally do from the top end ie we enter the woods from Holmewood area.
Just before this trail starts descending more steeply to the stream there is a narrower trail going off to the right. About 50 yards in there's a white sign on a tree telling you it's 60% black / 40% red and put in place by Bradford Council.
If you're on Strava the segment is called Down Hill Right Side Black Carr and can be found here: LINK
It's singletrack, fast and twisty - good fun, with a jump at the end.
As I say, we were amazed to find it.
For Calverley Woods we normally do the Rice Crispies segment (again from Strava) which is really good but there are loads of other trails in there.
If you're not on Strava it's difficult to describe but we get to it by riding up and past Clara Drive, through the gate at the end of the tarmac and turning left just before you come to a stone building on the left. Once you turn (onto narrower footpath) keep right all the time and you eventually come down to the canal side. Ride along for a while and then turn left uphill, it's all a bit overgrown at the moment here! You then head back up towards the central woods, lots of options here for trails.
Hope this helps!