Hello Candice,
THanks for trusting DoctorSpring.com with your health concern.
Frequent urination could be due to the prolapse also, as it presses on the bladder more often.
Cystitis would manifest as some amount of burning during urination, pain in the suprapubic region etc.
You can get it ruled out by having a complete urine examination, urine culture and a bladder scan.
At 62, any kind of bleeding should be looked into.
That said, you should feel reassured because the most common cause in this age group is atrophic vaginitis.
In this condition, the mucosa ( surfaces ) of the vagina becomes dry and fragile, due to lack of estrogen.
This makes it prone to infection , breakage and spotting / bleeding.
THe condition is easily diagnosed by a visual examination by a gynecologist, please have that done.
Treatment consists of lubrication during intercourse, and local estrogen therapy if the problem persists.
Have a specialist look at it, the bleeding should not be ignored.

All the best & Please feel free to discuss further.