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Bacteria can grow rapidly in warm water. It is possible that your morning dip uses up any residual chlorine left from the previous night's dose, and waiting until the end of the day to dose the tub allows anything left behind from your multiple soaks several hours to grow. IMO your 1 tbl dose is a little light, especially with the amount of use. Consider adding 1/2 tsp after each dip during the day, and a bigger dose at night, for a total of 1.5 - 2 tbl/day. The small doses should help keep things in check, but not create enough residual to bother you. If multiple doses is too much hassle, another alternative would be to dose 1 tbl after your morning soak, and another tbl at the end of the day.
I would be wet all day long.
Bama, I have a super sniffer...is the smell that you are detecting a clean fish-tank kind of smell...not nasty, but earthy? Remember, you are sweating while you are soaking too...and you don't instantly stop sweating when you step out of the tub..I know the one thing that I don't like is when my head sweats...I have noticed on occasion a non-chemical earthy kind of smell...but I usually shower or at least rinse after I soak.