Bristol is a great place for XC and all really close to the city. Aston Court has a lots of really good trails dotted around the place but the main marked trail is called the Timerland Trail, it starts at the gate house on the Suspension Bridge side. It probably takes about 1 hour to get around at a leisurly pace and there are lots of other unmarked trails going off it, info about it on
this website. The trail goes through 50 Acre Wood which also has some good trails its quite a bit smaller then Aston Court though.
Next to Aston Court is a forest called Leigh Woods which is bigger then Aston Court and has more trails but none of them are officialy marked so the best thing to do if your going there is to follow the gravel paths and just cut off when you see a trail or find a local and follow them around. At the back of the forest theres some quite technical downhill which takes you down to the towpath.
There is tons of cycling in Bristol and it takes a while to find it all, the best thing to do is just explore. I help build and maintain the trials in Aston Court with a voulenter group, there website is
here