No bleeding is ever normal, unless it is coming from the reproductive organs of an intact (not spayed) female cat in heat!! The blood can be a sign of stress, bacterial infections, parasite infestation, bleeding disorders and many, many other causes. Please take a stool sample to the vet (must be 24 hours fresh for best diagnosis) and do not delay--this is not normal!!! Good luck!
This happened once with Wiggies just after we changed his food. The new kibble was a bit bigger and more pointy than his old one. We called the vet and they said not to panic as otherwise he seemed fine. So we just kept an eye on him, gave him his old food and introduced the new one more slowly. He was fine after that.