This is what I found after a little googling. The important part, for this discussion, is this part:

"...Bleeding — Individuals who take aspirin regularly may notice bleeding for slightly longer than normal when they cut themselves or have a nose-bleed. This type of bleeding usually causes no significant problems..."

So, who knows, if we are talking a major type injury. I was a peace officer for 30 years, with the inherent risk of injury, and took a daily aspirin for the last ten years or so. The risk of a stroke scared me more than bleeing to death because of one aspirin a day...