How much is a bit? Some milky gear oil when you first pull the plug, or is the entire gear oil milky?
If its a little milky when first draining and clears up quickly, the leak is not big.
First check to do yourself is to check BOTH the drain and fill plug gaskets. Many times it is double gasketed. Also check the gasket seat to see if there is any residue of an old gasket there. You want that surface clean and bright. When you tighten the plugs, use the appropriate size screwdriver. Those slots are big, you wont get away with using a small screwdriver. You want something with close to a 1/2" blade to put the right torque on the plug. Hope this gets you pointed in the right direction.