Is temporary, brief bloody stool common? Do lots of people have it a few times in their lives?

Not common. Don't know your age, history, etc. Bloody stool can be seen with infection, poor blood flow, diverticulosis, polyps, fragile blood vessels, inflammatory bowel disease, cancer. Bright red blood on toilet paper often is from anal problems, including hemorrhoids, but also can be from more serious issues(see above). See your doc.