We don't buy bottled water cause most of it is just tap water anyway.
Garden hoses will give you a garden hose taste.
1/4 cup of hydrogen peroxide MIGHT get rid of taste but more than likely you will need to drain/flush fresh water tank and refill using a 'potable water' hose with your filter.
And if I can't use the water in my fresh water tank to drink then I'm not going to use it to wash dishes or shower. The skin is largest organ and will absorb the stuff in water while showering.