What kind of boat is it? Is it a factory live well? If so it should already have a pump. Also, the live well should over flow out the side of the boat, not into the bilge.
In previous boats I've owned, a plug would be inserted into the hole at the bottom of the livewell, the drain. Depending on the boat, the live well pump is mounted to the transom, or slightly forward and connect with tubing. It draws water in from the hole through the transom and pumps it to the spray head located at the top of the live well.
Once the live well is full, excess water is spill overboard via a tube and fitting in the side of the boat.
Then to drain the live well, you reach in and pull the plug. Water will then either drain out the same fill hole in the transom of the boat or like my boat it will dump out the bottom of the boat through the hull.
If you are spilling water into the bilge I have a hunch there is something missing.