I do not have a dry Bilge. There always seems to be some in there.
I think most bilges will acquire some water, over time. Heavy rains, wash downs, etc. I wouldn't think your bilge pump should run regularly though, once in a while, yes. Also, the bilge pump will not remove all of the water, so, having the OCD, that I do, I vacuum out the remaining water, frequently. Usually about 2-2 1/2 gallons sit down there after the pump is done. If you're getting more water than that, or the bilge pump is running regularly I'd check for leaks somewhere, shaft packing, raw water pump, leaking hoses etc.
I bought a cheap ($12) self priming diaphragm pump on Amazon, built an acrylic box for it and ran tubing from the lowest part of the bilge to the shower sump box. The pump motor is not brushless so I put it in a box to avoid blowing the boat up. Ended up putting it on a cheap timer to run for a few minutes every other day when we weren't on the boat. Worked like a charm! It would suck every last drop of rain, wash water and condensation out of the bilge. Thought about adding a sensor to it so it would know the start and stop but never found the need.
Thanks for that info and after I posted, i started looking on the forum and think I ran into your post with that info. I ordered a diaphram pump and was/am headed down the direction you went --- timer set (or some manual switch?) that I could set and let it do its job once a day or every other day for a few mins....... when you ran it to the shower box, how did you plumb it to exit actually out of the boat? You just pushing it from under the shower and to further back of the boat or actually into the shower box that's under the batteries area where it gets sucked overbaord?
I drilled a hole in the top of the shower box and put a barbed connection on it. The box has it's own float switch so when it filled up it ran on it's own and pumped the water overboard. I was in an SS though and my shower sump was located in the bilge. You might be able to tie it into one of the other overboard lines in the bilge fairly easily.
The timer was cheap enough so I went with that and adjusted it to every other day since there wasn't a lot of need for it to run every day. I never once returned to a wet bilge but the first few runs were a little hectic until it cleared the few random pieces of plastic and what not that I couldn't see in the bottom of the bilge. The diaphragm pump doesn't like debris and can't push it through.
I wouldn't consider any water in the bilge outside of rain/wash/condensation normal. You are collecting water from somewhere whether it be loose hose, leaky water tank or something else. 15 gallons is a LOT of water for no rain. If you are in salt, you can test the water for salinity after a thorough cleaning of the bilge. That would at least narrow it down.
Is the 1" the lower limit of the bilge pickup? Is it possible the pump is already pumping water off the boat and you just don't know it?
It will be interesting to see what others think but to me, there should be no water in the bilge unless it rains, you wash the boat or have a lot of people on/off the boat swimming. It might not be a water intrusion, it might be coming from the interior of the boat itself. You can dye your water and then run everything and see if the dye ends up in the bilge.