I would just make a rectangle wide enough to fit wrapped around the rail & long enough to give her cushioning cover however far up & down the rail she might hit. Bat it, quilt it, add velcro the length to secure it around the rail.
ETA: oops - just re-read your post & realized you are talking about the bracket not the rail. I should not speed read. Can you still do something similar to wrap around the bracket & secure using velcro?