Maybe something cool actually exists. Something clever. I was actually thinking of an hydraulic ram but im not sure it's a good idea. Another thing i saw was a one-way check valve. Would this work?
You can buy a mechanical pump that you work by hand for this purpose. It has a cylinder with a piston inside, a suction hose, and a discharge hose. You dip the suction hose into the bilge water, aim the discharge hose overboard, and push the handle on the piston back and forth like a bicycle pump. This is called a manual bilge pump.