A lot depends on whether you have a cabin bilge seperated by a bulkhead from the engine room/rear deck or a through bilge that runs the length of ther boat. If the former then no it isn't normal to have water in the cabin bilge.As you don't know how many days/weeks/months it has taken to get there I would use a Wet Vac to get rid of what is already there and see if any more appears. I would expect to hear the water pump cycling regularly if you had a leak on the water system. Some older boats were designed to have the shower empty into a trough bilge where it run to the back of the boat, so without knowing what you've got hard to say. It always looks worse than it is, I wouldn't panic yet.