I’ve started sticking up a few route guides on our web site. If I wanted to explore further field than Ashton Court then I’d try this one. It starts at Ashton Court but with a bit of road hacking you can join up some nice “grey” trails up the road and then some natural stuff even further afield. Just be aware that the unsurfaced trails will be very muddy at the moment!
Bourton and Beyond
If you’re in South Glos then you might find it easier to get to the trails in Bath or North Nibley. I think there’s a North Nibley/Kingswood route in the trail guide on this site actually.