You cannot bleed — or live — with zero blood pressure.
The absolute blood pressure must be at least 1 atmosphere of pressure or the atmosphere itself would clamp down on all your limbs like a blood pressure measuring sleeve and restrict blood flow. The blood pressure must overcome the atmosphere or blood cannot flow. So a blood pressure of absolute zero is not possible.
But I suppose what you meant was "blood pressure of zero compared to the atmosphere", which is what we normally mean. I am sorry but that too is impossible. There are 100 000 km of blood vessels in the human body, and getting a fluid to flow — especially a fluid as viscous as blood — requires a force to push it through all of these tiny tubes. Blood vessels always offer resistance — a kind of friction — to the blood, and this must be overcome to make the blood flow. You cannot have blood flow without blood pressure.
If you rupture a blood vessel however, then you have a path for the blood that offers no resistance. So simple physics say that this is where the blood will go, literally taking the path of least resistance.
So you have two incompatible demands here. In order to not bleed, you need zero blood pressure, but then no blood is flowing through your body. It goes without saying that this is very bad for you. Or you have non-zero blood pressure, but then you will bleed if any of your blood vessels are ruptured.