First of all, it's a stage that'll be over pretty soon. Second, she does sound like a wonderful, creative kid who can be a bit of a challenge!
One of my 3 earned the nickname "The Loop-Holer" when he was about 3, because he couldn't just accept rules at face value either. He was always trying to compromise or would find a loophole in a rule. It was equally funny and annoying.
My advice would be to let her make decisions whenever she can. And if her compromise could work, listen to her and let her win.
But when you need her to do something, just don't compromise. Tell her, "sorry, not tonight." It's OK to be firm, as long as you don't change your mind once you've said "no." And yes, that can make a kid like her mad. Too bad.
In the case of bath time, the problem with threatening to turn on the cold water is that she still won't get out and you want her out, right? So that's not solving the problem.
I might have agreed to 5 more minutes, but once that was over, it's over. I would have given a warning that if she didn't get out of the tub by the count of 3, she would lose bed time stories (or whatever the consequence). And then I would have calmly lifted her out of the tub kicking and screaming if necessary if she still refused to get out. When she screams and yells at the loss of stories, I would calmly say, "You had a choice to get out and you didn't. I think that's really sad, too. Next time, I hope you do what I ask so you can have stories."
I think it's important to stay calm and not let her get you mad. I really liked the advice in 1-2-3 Magic when my kids were that age, plus I used a little bit of Love and Logic.
