I respectfully disagree. Generally, fish do not evacuate (for lack of a better term) at a rate high enough to raise the ammonia levels in the water in a fishing days time. If there are enough fish in a livewell to do that then they will run out of air before toxic poisoning happens. If you go with just a bilge pump, that is fine, but remember that the water you are pumping into the livewell is warm (surface water). Warm water does not hold as much disolved oxygen as cold water. Thus you can't keep as much bait in the livewell.
My suggestion is to aerate and add ice to the water (this is why I suggested the cooler). And yes it is ok to add ice to saltwater. Just enough to keep the fish happy. If you are concerned about ammonia levels, then change your water every couple of hours. The cooler has a built in drain...remember.
However this is JMHO.
The Rodbuster