Wow I wish I had a nickel for every time I've heard this question. It's well worth asking though and something that should be answered before you ever head out to bowfish.

RB, we always try to utilize every fish we take. We don't eat many ourselves but we do give as many as possibleto folks who do. We have donated some to wildlife rehabbers and just yesterday gavedozens offish to a DNR biologist to use in a turtle trapping survey. We also use many as fertilizer for our garden.
When we can't find a use for them, we find an ethicalway to dispose of them. This means somewhere that won't disturb others. We have a farm field where we are allowed to put fish. The field is far from any houses so the smell won't be bothersome to anyone.
Getting carp out of the waterway is a benefit to the environment. Period. Duane Chapman, Biologist for the USGS, says that it is better to have these fish in the dumpster than in the water. What he meant is that just getting them out of the water is beneficial.
The bottom line is whatever you do, just don't leave them anywhere that would be offensive to others.
Hope that helps.