The hose that goes to the bilge pump and connects to the broken "flange" on your bilge pump goes outside of the ski, it is the hose that water pumped OUT of the bilge flows through. The bilge intake is on the bottom of the bilge pump, that's the part that sucks water out of the bottom of your ski. If all you did was hook a hose up to the broken part of your pump and you didn't run the hose outside of the hull, the pump would suck water out of its bottom and then shoot it back into the hull of your ski from the hose. continuously.
You need to pull the bilge pump out, and see if you can stick another piece of pipe to the broken flange. You might be able to find a piece of PVC pipe that will fit inside the broken "flange" or even outside, over the "flange." You will then have to adapt the bilge hose shown in Ernest T's diagram, to the piece you added to the bilge pump. It may be as easy or even easier, to replace the broken (old?) bilge pump with a new one. They usually cost about $30.00 but I recently sold one on eBay for $16.00, including shipping.
Good luck with your repair. You don't want to be out on the water without a dedicated bilge pump that will run even when the ski doesn't.
former sea doo owner, will never own one again