CO2 fluctuations from your tap water are pretty unlikely to cause BBA in a low tech tank, if it truly is low-tech.
More than likely, the problem is that your light levels are higher than you think(meaning you are a little more than low-tech lightwise), which is why BBA is rearing it's ugly head in your low-tech setup. You'd have a deficit of carbon, but adequate light and nutrients for any old opportunist to take advantage of.
What is the tank size, what type of lights are you running(and perhaps the distance from the substrate), and what photo period?