For those saying it's evil, imagine the following scenario: The PC doesn't kill the bouncer but ties him up and hands him over to the local law. The bouncer is put on trial for attempted murder, and on the PC's evidence, he is convicted. As the wronged party, the PC is consulted on the sentence; he argues for death and his arguments are accepted. The bouncer is hanged.
Still evil? If not, what's different? What I just described is essentially what the PC actually did, except it's taking the lawful approach (do it through the courts and proper authority) instead of the chaotic one (do it yourself on the spot). Why are the PC's actions inconsistent with, say, Chaotic Neutral?
First off, the bouncer had yielded, dropped his weapon, and had his hands in the air. The act was evil, plain and simple, and I can't quite believe there is actually a debate about that. It's flat out murder.
If he was lunging at the characters, or anything like that, then OK, a case for self-defense. But the danger had passed.
So in your court case example, I'd say it's still evil, just a society sanctioned evil. A death sentence for attempted murder? I would expect good characters to potentially be fighting the injustice in the system if possible.
To put it a different way, if the law of the land is the Nazis and you turn them over to the law - yep, evil act.
If the courts are reasonably fair, with a possibility of the death penalty, but also other possibilities, then that's quite different. Although I don't see a judicial system with the possibility of the death penalty for attempted murder as "reasonably fair."
If the law is fair, but he's convicted and given the death sentence because the player lies? Evil.
If the bouncer had committed murder, then surrendered, and the characters still killed him? Murder. Evil.
Turned him into the law knowing that he would potentially face the death sentence? Not evil. Knowing that he would definitely get the death penalty, as long as it's a question of the evidence and if found guilty, that's fine and significantly different than committing murder.
The things that always rate as evil acts are murder, torture, slavery, raping and pillaging, etc. Once the bouncer was no longer a threat, then killing him is murder. If the law is oppressive and evil, then using the law to commit the murder is still murder.
Is the character evil? Well, that's somewhat debatable...I guess. A single act doesn't necessarily make somebody evil, but murder pushes you a whole lot closer. There would have to be quite a bit of redemption.
Would anybody here seriously continue to spend time with a person that did that very thing in real life? Even if he was my best friend, I'd be telling him to drop his weapons and surrender to the police. Unless it was the Nazis. But that would be a game changing move between us.