So filling in some blanks here, I assume you mean water to mix into syrup? if you are concerned, most homes have a way to get water ahead of the softener. Even some of the outside hose connections are pre softened. I would be concerned with the city water that is chlorinated. Not sure on that one , others can offer input. I have not fed in a long time so do not have empirical evidence.Does having a water softener effect the bees, I know for plants and your lawns it's bad.
If you leave tap water in an open container most of the chlorine will "evaporate" off fairly quickly. This is why water left outside in the open will start growing.I would be concerned with the city water that is chlorinated.