What if I had eaten about three hours ago and bits of the recognizable undigested food I had just eaten are present in my stool?

Undigested. It generally takes much longer than three hours for ingested food to appear in bowel movements as the food has to traverse many feet of intestine first. Three hours would signify exceedingly rapid transit. The bits you observed probably were ingested a couple of days earlier unless you are experiencing vicious diarrheal activity. For chronic bowel concerns, a gastroenterologist is best qualified.