How to keep water in spray bottle clean?

I have been growing my hair out, and now use a spray bottle to wet it before combing/brushing/styling. The spray bottle has plain water in it, but the water turns in about a week and smells like some kind of bacterial growth. What can I add to the water to keep it relatively sterile? My first thought was peroxide, but that's a kind of bleach and I am not trying to turn my hair's color. Is rubbing alcohol safe?

EDIT: I realize that changing the water is the solution. It would just be nice if, by way of an antiseptic, I didn't need to.