Hey Andy, I wouldn't buy a cheap sandblaster for cleaning rubber bumpers, although a sandblaster is never a bad idea for other parts. I've used plastic stripper, a product available from several manufacturers, I used Marhydes aerosol with good results. You could remove the paint with a DA and a light abrasive like a 280 or 320, but, be careful, plastic isn't that solid and making a mess is quite possible. Another way is brake fluid, brush it on, let it sit for a few hours, remove the paint and thoroughly wash, clean and dry your bumpers. Whenever stripping bumpers be careful, try a small unnoticeable area first, just to get the feel and effect, when comfortable move on to entire piece.
Hope this helps Andy