How do I remove mildew/mold from vinyl air mattress?

I bought a small "aero bed" for my 3yo to sleep on when we go away.. it has worked wonderfully up until a month or so ago when, upon pulling it out of it's bag, I noticed that there were NUMEROUS large spots of mold/mildew (moisture must have entered the bag somehow and started this growth). Now, the mildew/mold is on the "soft" side of it and not the "rubber" side so I know I need to be careful about what I use, and don't think I can just use bleach, etc. bec. of this. Any advice for how to remove this?