Their is no time period where all unwanted chemicals and elements will evaporate from the bucket of city water. Many of the unwanted items could be: Chloramines, copper, silicates, fluoride, arsenic, iron and manganese, sulfates, barium, lead, nickel and the list goes on and on. A good city water plan will still have ~ 3 - 4 hundred ppm of dissolved solids, where an aquarist is looking for 0.0 ppm of TDS
If you can't do RODI then stick with the distilled water and hope they do not incorporate copper in the steam generator.