Thank you for the additional information.
There are a couple of things that might be going on here, all of which will require a vet visit to help you sort out.
From your description, it sounds as though the spots of blood are coming from her vulva, most likely in the form of blood in her urine since the blood spots become diluted.
The spotting that you see where she's been sleeping likely occurs to some urethral sphincter incompetence. Older females that have been spayed,and especially those that had been bred prior to spay, can develop a weakness of the muscle
that helps to keep the bladder closed (urethral sphincter). As a result, there can be leakage of urine from the bladder, especially when the pet is at rest and the muscles are at their most relaxed. Urethral sphincter incompetence can be treated with a medication called phenylpropanolamine daily or one called DES a couple of time per week- this is lifelong therapy.
The blood in the urine may result from a urinary tract infection (UTI), which could secondary to the urethral sphincter incompetence. Since the sphincter is open, it allows bacteria within the vaginal vault to ascend the urethra and enter the bladder to cause infection.
The UTI may also be secondary to crystals or stones within the bladder that cause irritation of the bladder wall, resulting in bleeding and increased risk of urinary tract infection.
A final possibility for blood in the urine is a tumor of the urinary bladder called transitional cell carcinoma.
Other possibilities for blood from the vulva include a vaginal infection, an infection of the small portion of the uterus that remains after spay, or a mass in the vagina.
Your girl will need to be examined by a vet and have a urinalysis done to find out if there is a urinary tract infection. Imaging of the urinary bladder (either x-ray or ultrasound) is also recommended to help rule out bladder stones or masses within the bladder or vagina.