I suspect the aerated bucket approach works by allowing more atmospheric CO2 to dissolve in the water (forming carbonic acid).
In any case, these techniques allow for mild changes in pH, but you're not going to see a drastic drop. Also, the more alkaline your water is, the more it will resist changes in pH. You can see this in blackwater rivers as they reach the sea- the color drops out at a very low salinity, due to the acids being neutralized by the alkaline seawater. So, if you want a big drop in pH, you're probably going to be better off using reconstituted RO/DI water.