Most gunshot wounds do not bleed immediately. It takes a few seconds for the blood to flow from and injury. Have you ever cut yourself deeply? There is a good 5 to 10 seconds before the cut begins to bleed. Gunshots to the chest even more so because the chest cavity has to fill with blood before the it is forced from the bullet hole.
When Ronald Reagan was shot he did not bleed extrnally at all for several minutes. So your assumption of blood on George is wrong. Due to two sweat shirts being worn there would not even be blood splatter from the initial impact.
So then Dexter can be told to stay home? :)