Get a shower over the bath. That way whatever happens in the bath can be rinsed away in a cleansing stream immediately. Also, it does not matter whether there is any piss in the bath as:
a)skin is water tight
b)I don't drink bath water
c)The dilution would render toxins harmless anyway.
And regarding having one off the wrist - don't you find it sticks to you in such a way that only the harshest of power showers would remove it. Especially from hairy areas.