clay could actully be a problem, i used to do mine in the basement and after a few pump outs through the drani etc i found that the clay although 100% diluted still formed a silt in the ubends etc
so maybe over a period of time it could build up, also a bath tub is only so big, to have any fun you will need to fill it half wayish with clay
leaving a thicker mass to get rid of
i should think it will all go and be washed away but it might build up over time
once the clay settles for a little bit it starts to build up
in london uk i get my clay from "cerematec"? or used to, they are in north london and a clay supplier , i think in or off Queen street, edmonton / tottenham.
pure bought clay is good and cheap from such places, sure beats trying to get it home from the side of road works then sifting the stones out, but thats another messy adventure
mind you if you aint doing the mud bath actully in the household bath then you dont got to worry about washing it away at all, i kept my clay around for ages, till i needed the space