For the rubber bumpers try something like a natural degreaser/cleaner, like one of those citrus orange cleaners. You could also try a natural hand cleaner like fast orange or anything natural that removes grease like from working on a car. I think all those will be safe for the rubber and you can work it in with your hands or a brush.
I'd still test it on a small unseen area before cleaning the whole thing just in case, better safe then sorry.