While paying attention to sanitation is really important, if it were me, I would not worry about it, although if you are boiling the water I would just give each bottle a quck rinse with starstan before filling the jug. If you were using municipal water I would not even bother boiling, the chlorine should be enough to keep the water it self sanatized (that is why it is there).
It sounds like you are doing partial boil? If you are really worried about it I would try to move to full boils, in addition to alleviating any concerns it will also improve your beer in may other ways.
And to add a random bit of trivia, municipal water is actually held to higher standards than bottled water. Bottled water only needs to list the ingredients (water), public water supplies (which include municipal water) have to be held to a long list of quality and safety standards. In practice most bottled water is actually municipal water (check the label most even admit it). If the taste problem is chlorine (most people who dislike their water it is chlorine) it will get off gassed during boil and fermentation.