Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Missy has blood in her urine and is having some accidents, one on a plastic bag. I think that she is definitely trying to get your attention and tell you she is uncomfortable.
Cats can have blood in their urine due to an infection, crystals or calculi in their urinary tract, or even a mass in their urinary or reproductive tract.
Cats with sterile inflammation of the bladder (Interstitial Cystitis) can have an inflamed, thickened bladder lining that bleeds.
Cats tend to be poor drinkers and as such have very concentrated urine which can allow irritating crystals to form in her urine, which can lead to calculi forming.
It sounds like she straining to urinate, only passing a small amount and urinating frequently.
Is she licking her genital area more then usual?
Is she eating normally?
I know that a veterinary visit isn't easy on many kitties but this is something that we may be easily able to fix and if she is having accidents that means she is likely uncomfortable and experiencing inflammation and urges to go.
I don't think this is an emergency tonight, but if you can get her see tomorrow morning that would be ideal.
Being female (short urinary tract) and older (weaker immune system) and her accidents an infection is very likely, and that we can help easily in most cases. I would start with a physical examination and urinalysis with culture to see if she has a health problem. Depending upon her examination findings radiographs and/or an ultrasound of her abdomen to evaluate her kidneys and bladder may be recommended.
It is possible that she has calculi (stones) in her bladder too, that may require surgery.
Worst case scenario is a kidney infection or a tumor in her bladder.
You can choose how involved you prefer to get with diagnostics, but a urinalysis with culture is relatively inexpensive and usually is enough to get us started in helping her.
Best of luck with your girl, please let me know if you have any further questions.