Gastroesophageal Reflux Disease (GERD) or Peptic Ulcer Disease: Given the history of vomiting bile and abdominal cramping, along with the presence of blood in urine (which could be related to a systemic response to pain or a direct effect of a gastrointestinal issue on the urinary system), a gastrointestinal issue seems plausible. The absence of a gallbladder might reduce the likelihood of certain biliary causes, but GERD or peptic ulcers could explain the symptoms, especially the vomiting that tastes like bile.

Irritable Bowel Syndrome (IBS): The patient reports abdominal cramping, bloating, and changes in bowel movements, which are classic symptoms of IBS. However, the presence of vomiting and blood in urine might suggest a more acute or severe condition.
Diverticulitis: Lower abdominal/pelvic pain and changes in bowel habits could suggest diverticulitis, especially if the patient has a history of diverticula. The intermittent nature of the pain and the presence of blood in urine (possibly indicating a urinary tract infection as a complication or an unrelated issue) make this a consideration.
Urinary Tract Infection (UTI) or Kidney Stone: The blood in urine and the abdominal/pelvic pain could be indicative of a UTI or a kidney stone. The presence of urobilinogen in the urine might suggest a gastrointestinal origin of the symptoms affecting the urinary system indirectly.

Appendicitis: Although the patient's appendix might have been removed (not specified), if it hasn't, appendicitis is a critical diagnosis not to miss due to its potential for severe complications. The lower abdominal/pelvic pain and vomiting could be indicative of appendicitis.
Bowel Obstruction: Given the history of abdominal surgery (gallbladder removal), there's a risk of adhesions causing a bowel obstruction. This condition is a medical emergency and could explain the vomiting, abdominal pain, and changes in bowel habits.
Ectopic Pregnancy: Although less likely in a 56-year-old female, it's not impossible, especially if the patient is still menstruating. Lower abdominal/pelvic pain and vomiting could be symptoms of an ectopic pregnancy, which is a medical emergency.

Carcinoid Syndrome: This rare condition, often associated with neuroendocrine tumors, can cause abdominal cramping, diarrhea, flushing, and wheezing. The presence of intermittent abdominal pain and changes in bowel habits might suggest this, though it's less likely.
Inflammatory Bowel Disease (Crohn's Disease or Ulcerative Colitis): While these conditions can cause chronic abdominal pain, changes in bowel habits, and weight loss, their onset at the age of 56 would be unusual, making them less likely but still possible diagnoses to consider.