Plastic shower dome has outside mold

There are some sprays available for killing mold & mildew. I had some when I had a boat. I can't recall whether the label said anything re plastics. So, look in the boating section at a Wal Mart or other store and see what you find.
I know you can also find it online. Do a search for "mold & algae sprays" at Amazon, and you'll see a list of products to check out which you may be able to buy locally.