The Dream Ball can only be obtained when in an encounter with a Pokemon caught through the Dream World, and can only be used in that encounter alone.
It will appear in your bag, but if you don't use it, it will disappear (l tried it already).
Either use it during that encounter, or use another ball and let it disappear.
By the way, one Dream Ball comes in your bag every encounter with each Pokemon, so no need to save!
You should use it for convenience.