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After thinking about this, I think the outfits are made of extremely thin material, and they're all packed in her bodice. Notice how padded it looks, and that she always has some kind of ruffles or lace or bits of fabric on the chest area of all of her dresses, to distract your eye from the bulk there. She loosens the top of the dress she's wearing, and the dress under it falls free. The dresses are all sewn together, so that the outside of the bodice of one dress contains the inside of the skirt of the next dress, and she peels them off one by one. Like layers of an onion. That's why you don't see any remnants of discarded dresses lying around - because she's still wearing them. It's all one elaborate outfit.
I actually saw this live on the show, the one time we watched and it was awesome then (ten times better than the comedy yogi). The worst thing about that show is Hasselhof and the really, really pathetically bad "acts" like the guy dirty dancing with a blow up sex doll.