I am a very constipated person, and was wondering if its normal to have a lot of mucus and some bloody mucus come out when i have a bowel movement?

No.: While straining might cause worsening of hemorrhoidal disease, which can present as blood in the stool, i wouldn't expect bloody mucous. I would see your primary care doctor to see if you have hemorrhoidal disease and whether you need a colonoscopy or not, a procedure that a gastroenterologist or colorectal surgeon can perform.

Mucous/Bloody Mucous: While constipation may lead to disturbance of the lower GI tract, the passage of mucous and/or bloody mucous should be evaluated by a GI specialist -- stool tests, blood tests, and visualization of the lower GI tract by colonoscopy are all useful in determining a true diagnosis.