How long should it take for hormonal birth control to help with menorrhagia? I've been on it for a month and sitll bleeding heavily all the time.

2-3 mnths. It takes about two to three mnths for the hormones to decrease or thin out the lining of uterus ( responsible for menstrual bleeding) hence decrease the bleeding.
Another cycle. Give it another cycle or two. If still excessive bleeding, see gyn for an adjustment to hormone dose. If you feel faint weak or excessively tired see your doctor to be sure you haven't become anemic.