How serious is rectal bleeding?

Rectal bleeding. Rectal bleeding is often due to hemorrhoids. However, there are other causes that are very serious including cancer. In general, rectal bleeding should be discussed with your doctor and perhaps be consulted for a colonoscopy, especially if you are near the age of 50.
Complicated answer. There are so many factors that go into trying to decide if "rectal bleeding" is serious starting with defining what you mean by it. Factors that providers look at include bright red or not, only with BM or not, on tissue paper or stool or toilet water or all 3, pain or protrusion or painless, change in bowel habits like constipation, patient age and family history. Never assume it is hemorrhoid.
Perhaps very. The most common causes are hemorrhoids or anal fissure, neither of which are serious. Colitis and colon cancer also cause rectal bleeding and these can be quite serious.
Varies. Hemmoroids is not a big deal. Ulcers is a moderate deal. Cancer is a big deal. Get checked out asap!