It is good that you ruled out parasites or worms as that is the first step. I just want to mention this because there is one worm that can caus bleeding in the stool that clinics often don't find under the microscope - a tapeworm. This is caused by ingesting a flea - so if you have any doubt that this could be the cause I would simply purchase an over the counter dewormer with the active ingredient praziquantel and dose this to your cat according to the weight. It won't hurt anything if she doesn't have them. I would go ahead and do this just to rule it out and play it safel
Secondly, mucus and blood in the stool indicate colitis. Sometimes this happens as pets age a little bit, or with a change in diet, or with parasites. If you want to try and treat at home I would add fiber to the diet in the form of adding one teaspoon of pumpkin pie filling to the food each day. I would make sure she is eating cat food only, no table food or unusual treats and you can even put her on a diet for colitis which is called Purina DCO your vet may have.
If this doesn't do the trick, I would collect a sample of the stool in a bag that has the mucus and blood in it for your vet to observe and they may need to do some further testing to determine the cause.
After the praziquantel, fiber, and diet change I would expect to see improvment within a week.
Let me know if you have more questions,
Purina DCO I believe comes in canned. Other optiojns would be Science Diet I/D, Purana HA or Purina EN. Short of that any regular adult food would be okay.