Birth control that contains estrogen and progestin (the combined birth control pill, the patch, and NuvaRing all contain both) suppresses ovulation. So if you're using it correctly, you shouldn't be ovulating at ALL on it.
You cycle on birth control is very different from your cylce off of it. You don't ovulate, the uterine lining stays very thin, and your cervical mucus changes. Your period will not come when it would before you were on the pill, it will come during your hormone free week. That week is the fourth week of pills (or the pill-free week), the week without a patch, or the week without the ring. When you stop taking the hormones, your uterine lining breaks down and you bleed.