I have found the best way to actually clean white shoes is with Soft Scrub cleaner and a small scrub brush. Just wet the shoes (in a bathtub or shower) and apply the Soft Scrub and scrub away. Takes a couple minutes a shoe to clean and then just let dry after you have rinsed off. I learned this while working at an athletic shoe store years back.
As far as the bottoms, maybe let them sit in bleach for a while? (Just the bottoms, not the whole shoe)