Bleeding is never acceptable side-effct. You mentioned constipation, so probably the bleeding is from hemorrhoids. (If you type the word into your search engine, you can find hundreds web pages about this very common problem.)
Here is a short version:
"The term hemorrhoids refers to a condition in which the veins around the anus or lower rectum are swollen and inflamed. Hemorrhoids may result from straining to move stool.
Hemorrhoids usually are not dangerous or life threatening. In some cases, hemorrhoidal symptoms simply go away within a few days. But in most cases, hemorrhoidal symptoms eventually return, often worse than they were before. Although many people have hemorrhoids, not all experience symptoms. The most common symptom of internal hemorrhoids is bright red blood covering the stool, on toilet paper, or in the toilet bowl.
Hemorrhoids are very common in both men and women. About half of the population have hemorrhoids by age 50. "

(from: http://www.hemorrhoid.net/hemorrhoids.htm)

It is important, bleeding could be sign of much more serious conditions. Usually if the syptoms do not go away after 7 days, it recommended to check it with a doctor, even if it is "only" a hemorrhoids.

Meanwhile taking more fiber to prevent constipation can be the best thing you can do.