I would definately go to the ER if it doesn't stop on blood thinners. I have a scar running the length of my shin from the first time I shaved my legs (double headed razor, anyone remember them?)
I think the problem you're having is that when you pull the bandage off, your damaging the skin. There is a product out there called second skin or new skin (one is for burns and it's awesome, not that one). This you paint on, it smells like nail polish, and BURNS LIKE HELL. But it will give you protection and you do not have to worry about changing the bandage.
Another thought is to put Neosporen (sp) on the wound so that it does not stick to the bandage, and you pull the "scab" off every time you change the bandage.
Be careful of that area in the future. I cut my leg 25 years ago and if I hit is with a razor just right again, it bleeds like a stuck pig. At the time, my best friend was VERY helpful, brought me her dad's shaving stick, burned like hell but it stopped the bleeding.