When your not getting enough blood to the brain, you faint. It's your body's way of making sure your head is below your heart so that the blood doesn't have to push as hard to get to the brain. Being hot makes your blood vessel dilate, so If you have low blood pressure already and then have a hot bath, your blood vessels dilate and that combination can cause you to faint. Adding to those two things is standing up quickly, your body doesn't have enough time to compensate and get the blood to your brain quick enough contributing to the light headness and subsequent fainting. Sometimes just the hot bath and standing up too quickly is all it takes for some.

If you feel like you are going to faint you need to put your head below your heart. Either by lying down or putting your head between your legs. (Laying down reduces the risk of injury!) Some people are fainters, they are just more prone to it. But if it's not usual for you then maybe worth mentioning to the dr.
I seem to faint if i am sick and exert myself too much or have codeine!

Did you hurt yourself?