When I had my uterus removed, I had very light bleeding for about 2 days. If you are just getting your ovaries/cysts out, your period could be off for a few months. When they remove an ovary or cyst, it can mess with your hormones and therefore mess with your period. When I just had a cyst removed, I didn't have any bleeding. Nor did I when I just had an ovary removed. Everyone is different so these would be good questions to ask your doctor.
If you do not lose the uterus, you could have a much heavier than normal period that could be on again off again for about two weeks. It's not the same for every woman.
If you lose the uterus, I really don't know. Much of the bleeding comes from the uterine lining, but that would be gone. That needs to be asked in the hysterectomy forum.