Churchill Hall is only a short walk from the other Stoke Bishop halls, the downs and the Avon gorge, and just under 2 miles from the University precinct. The Google residences and precinct map gives the location.
Exit the M5 at junction 17, signposted for (Bristol W) Clifton, Severn Beach and Zoo, keep over to the two right lanes of the exit road (marked A4018). At the lights, take the A4018 signposted for Clifton and the Zoo. The dual carriageway continues past the third roundabout (with the 'The Old Crow' pub to your right). Drive straight up the hill (on the brow of the hill the road becomes single carriageway). Carry on for about three miles through three sets of traffic lights. Go past Badminton School behind a high stone wall on the right, onto the next (White Tree) roundabout. Turn right down Parry's Lane, and take an immediate left onto Saville Road. Follow Saville Road for a mile until you reach a set of traffic lights. Turn right and travel down Stoke Hill for 300 metres. Take a right into Stoke Park Road and Churchill Hall is on your left hand side.
The Maps and travel information pages provides details on how to get to the University.