In the bath: I don't take baths, but if I did, then no, I wouldn't piss in the bathtub. But as mentioned by others, bath water in and of itself is more infested with bacteria and other filth than your piss is. In fact, pee is naturally sterile (contains no infectious agents). If your pee did contain infectious agents, then you'd have a urinary tract infection.
In the shower: Definitely. I aim straight for the drain. And pee is cleaner than the dirt you wash off your own face every day.
Protip: It's actually beneficial for women to pee in the shower because it's one of the few places where a woman can comfortably pee standing up. In standing position,
the urethra leading out of the bladder is at the very bottom of the bladder (inferior to the bladder). When a woman sits down, the entire pelvic area, including the bladder, is tilted such that the urethra is pointing slightly forward instead of straight up and down. This makes it so that the "hole" leading out of the bladder is no longer located inferior to the bladder, but kind of anterior to the bladder (in front of the bladder) instead. What this means is that a woman sitting down can't get rid of all the pee in her bladder and it just stays there until she has to pee again.
In simpler terms, what's the better way to drain a bowl full of water--by punching a hole at the very bottom of it, or by punching a hole on the side of it? If you punch a hole on the side of the bowl, then the water will only drain down to the level of the hole. Any water below the hole will remain in the bowl. That's what's happening when a woman pees sitting down. This normally doesn't cause any health issues, but sitting down while peeing
can lead to more urinary tract infections than if a woman were to always pee standing up. By sitting down, there's always residual stagnant pee in the bladder.
Just sayin.