I am sure you are trying to be green and live off the grid, and all that crap. Silly me, I still believe the plumbing codes are there to protect the health of the nation, and what you propose would make an inspector faint!!!!
Once the water enters the tub drain, it is GRAY water. If you think it is sanitary, tell me what is rinsing out of your armpits or buttcrack! Codes like the UPC are now friendly to gray water reuse, but for sure, the one thing gray water can never do is touch a human .
If you are serious about this, we will not talk you out of it, but if you are in any kind of larger city where there are inspectors, etc, or if you ever plan to sell that house, I would reconsider that plan. There are other energy saving devices, like heat recovery systems on the tub drain pipe, that you could look into.