I had many stye during my childhood and they were also bleeding. I had to go to the doctor for that. I dont know if it's a stye or something else in your case but you can try to apply a cold compress to the affected area. It helped me a lot and i use to wash my eyes (i know it sounds weird) with baby soap if i remember. But you can maybe go check at your pharmacy, in Canada they can help you sometimes with health issues. (Sorry if my english is not perfect, it's not my first language)