You could always install a manual bilge pump and locate the intake at the lowest point in the bilge where the water collects. I installed one years ago that can be operated with a detachable handle in the cockpit. I've never had to use it. Mine was made in Rhode Island and I think it's a Gusher. Why are you getting water in your bilge? Is it coming from your ice chest, or do you have water leaking in from somewhere?
As I pointed out to you, I have a manual bilge pump and there are a couple of types that you can buy on the market. Mine is the type that needs to be installed with hoses and a thru hull outlet. I haven't used it in years so I'm really not sure if the rubber diaphram or the gaskets are still in working order. Oh I suppose that I could test it with a bucket of water, but I just haven't gotten around to it, but where you have some debri in your bilge, if it were me I'd buy one of those cheap plastic hand opperated bilge pumps because they always work. I think that they will pump water with a certain amount of debri in it without clogging. You could have the outlet hose drain into the cockpit and let the selfbailing hose in the cockpit discharge the water. For the amount of use that you're going to get out of a bilge pump, a simple plastic bilge pump that you can buy at "Worst Marine" will work great for you. I always carry two buckets on board my boat. If the pump don't work, the bucket will.