The Super Clean de-greaser is good for de-grucking oily engines, transmissions, and parts; it probably works on getting wax, etc. out of your polishing bonnets, but I wouldn't be sure it won't substantially damage the wool polishing bonnets in the process.
I wouldn't handle that cleaning task in a washing machine to start with. A pair of rubber gloves and and a utility sink with a hot water supply are where I do mine. Dawn dish-washing soap rubbed into the sponges and bonnets with a bit of water will take out a lot of stuff. Once you have a pretty good suds rubbed into them, rinse well, and repeat as necessary. It's a 10-minute task after using an applicator sponge for me. If you want to throw them into a washing machine with some Woolite after you've gotten the biggest load of wax and dirt out of them (I wouldn't skip the Dawn hand-washing step, particularly if you're not the primary oversee-er of the washing machine---she who is will not be pleased to see a ring of waxy, oily residue decorating the high-water mark on the machine's agitator and wash drum), I suppose that's do-able. Set them out/hang them to dry, and they're good-to-go again in a couple of days.
