The risk seems low, as Pepto Bismol does not contain aspirin.
However -- someone felt strongly enough about the issue to put a warning on the bottle, and so you should take it seriously.
There is a FAQ about the warning on their website. Its good readin.
Reye's syndrome starts with heavy vomiting, lethargy, and confusion. If you feel any of these symptoms, see a doctor immediately.
(Swampy isn't a doctor of course, and you might even consider asking your real one what to do, as that person probably is better informed).