Ladies, I need tips. How does one stop the bleeding on a lengthy cut?

Actually, what it is, is a SCRAPE -- really, it wouldn't be a problem on a normal person, not really any worse than a paper cut. I, unfortunately, am on blood thinners, and so even paper cuts bleed horribly.

It goes down a goodly part of the back of my calf, so there's no chance I have enough bandaids to cover it. I have an Ace bandage on it, but that's starting to bleed through. (Not all the way, just a bit, and it seems to be contained, but still visible.)

Ideas? Suggestions? Helpful hints? I'll be darned if I'm going to the ER for a stupid SCRAPE!