Food pieces in your stool is quite common with IBS. Are you sure you didn't eat anything with tomatoes or red peppers in it? Also, Kool-Aid will color your stools red.
You should always be on the lookout for black stools; that's usually a sign of blood somewhere in your digestive tract (unless you are taking Pepto Bismol, which will make your stools dark/black). Most bright red blood is just from hemmies, although maybe from an anal fissure. If you're not hurting down low, then it's probably internal hemmies (mine bleed a little sometimes, but don't hurt--just itch when they are healing up!). If you are hurting, then get looked at, because if you have a fissure, you may need some medicine to make it heal, your hemmies may be bad enough to need medicine or even surgery, or you may have something wrong with your intestines very low down.