Now that I've seen the picture I see that it is a type of hook and bungee system. The hooks don't appear conducive to putting a rubber band on each one. However all is not lost.
It looks like a larger rubber band that encompasses the entire plastic piece that comprises the hooks would work.
Another option that I would consider is drilling a hole in the plastic piece between the 1st and 2nd and 3rd and 4th hooks, and use two Zip-Ties per bag for security. But using this method the bags are not going to be as easily removable from the rack.