You've already received some excellent advice - isn't this site great? Just thought I'd add some of my experiences too.. I also deal with increased GI problems with my periods. I have endometriosis, which causes me to deal with lots of pain, and the IBS symptoms on top of the pain can often be overwhelming. Therefore, I completely understand your situation.
During our periods, prostaglandins are released, which are hormones that cause contractions of the uterus. Also, however, the prostaglandins can cause cramping of the GI tract and lead to diarrhea and intestinal pain. Non-steroidal anti-inflammatory drugs, like Advil (ibuprofen), inhibit the production of prostaglandins and often help with uterine cramping. I've also noticed that Advil helps my intestinal problems as well. Have you tried taking Advil during your period to see if it helps with your intestinal cramping? It may be worth a try, if you can tolerate that class of drugs.
Also, I agree with everyone that you should definitely talk to your doctor about possibly changing your BCP. Often, women have to try several different brands, with differing hormonal levels, before they find the one that works best for them.
Good luck, and take care.