Recent discovery of bleeding cyst/endometrioma. Previous cyst drained from same ovary after hysterectomy +2 yrs. What's probability of surgery?

Try med treatments. Endometriosis (in ovaries or in the pelvic-abdominal cavity) can be very difficult to treat medically and even by surgically removing both ovaries. Draining an endometrioma/bleeding cyst may only provide temporary relief but no cure. Ask your Gyn if medical trials with GnRH drugs, progestins or other medications would be valuable before (or to avoid) returning to the operating room again.