The vinyl should hold up well to the bleach, however if there is any cotton based stitching holding things together, the seams may come apart very quickly. Especially if there is any age on it.
I have had some success with removing mildew,and stellar success removing general dirt/grime/grease from vinyl with Mr. Clean "Magic Eraser" a relativly new product, looks like a foam sponge. Some of the boat upholstery I've done looks cleaner than when it was new. You'll find it at your local supermarket. You also wouldnt believe the job it does on lots of other things.
