Important if it is salt water or fresh (assuming your boat is floating in salt water), and I don''t know from your post which it is.
If salt, consider thru-hulls, etc. This should probably go to the top of your list. I once had a VERY small hole (e.g. a hole from a removed screw) that was above the waterline until the boat moved, then it was under--it put a LOT of water into the bilge once covered it--it was surprising. So check for this. Rudder post or packing gland for the engine shaft are also potential hot spots, when running.
If fresh, two prime areas--rainwater (could be from anywhere). E.g. leaking hatch, etc.
OR, a problem we had--if you have a pressure water system with hot water heater, and the hot water heater pop-off valve dies, it could dump fresh water into the bilge and then the pressure system just refills it. Check if your water tanks seem to be going down quickly. IN any event, somewhere in the fresh water system could also be the problem.
I also like the talc idea--thanks Gord.