Is it true that some patients with endometriosis have bloody stools, bloody urine, painful urination and painful bowel movements?

Yes. The presence of blood in the urine, stools, painful urination or painful bowel movements could be due to involvement of these organs with endometriosis but other conditions such ass ic, other tumors of the bladder or bowel need to be excluded. Inflammatory bowel diseases like crohn's/colitis needs to be excluded.
Yes. It can happen but also part of the differential are processes known as interstitial cystitis and irritable bowel disease, inflammatory bowel disease. Usually a gynecologist working in concert with a urologist and/or GI specialist can help pin down the diagnosis as each is treated relatively differently...Endometriosis can invade the rectum, (or bladder) and cause bloody, painful stools.