(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).
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.