The Downs Way is the new name for the long-established National Cycle Network route 4 into the city. It’s essentially just a set of residential roads joined together; still, the section across the Downs and along Hollybush Lane is enjoyable, and the extra mile on the five-mile journey is arguably worth it to keep away from the busy A4018.
As an alternative route between Henbury and Bristol, you can use the permissive road through the grounds of Blaise Castle. This is slightly shorter, has the same amount of climbing, and avoids some of the faffing on residential roads.