Ok, since it is a bathtub, you could fill / drain it with filtered tap water and clean it between uses. Doesn't have to be a continuous, closed system. That also negates the need for filtration...this gets even more do-able. Might not even need a bathtub....one of those lozenge shaped galvanized livestock watering tubs mightwork also. Though that option would need some sort of back / shoulder rest in it. And they have a bottom drain also.
Richard
Richard