Most physicians now perform endoscopic browlifts, which involves placing about 4 small incisions in the hairline. The bulk of the surgical work is done through these ports, and then the brow is fixated to the bone in its new position. Usually the amount of bleeding is minimal. Bruising is usually noted in the lower eyelids, because that's where the blood pools. It takes about a week for all the bruising to resolve.
Before surgery, make sure you discontinue foods and vitamins that can cause increased bleeding (your physician should provide a list to you), as well as aspirin, motrin, advil, blood thinners, etc. You may benefit from the use of Bromelain postoperatively, which helps decrease the bruising. You may hear about taking Arnica montana, but in my experience, it does not help as much as Bromelain.