You might want to stiffen up the side of the bag that is against the rack by slipping something in the bag on that side. If you aren't concerned with quickly taking the bags off and on the racks, you could even tie the bags to the rack.
You will want something to attach the bag to the bottom of your rack to keep them from bouncing off. Many systems do use a bungee. My kitty litter buckets bounced off a couple of times before I addressed that issue!
Do you have pictures of the bags?