Overwhelmingly, after.
I've never heard of "settl[ing] in bad faith" (although see my comment below regarding a "good faith settlement"), so I don't really know what that might mean. However, I'm skeptical that having a judge "sign off" on a settlement would prevent that. I'm also not sure what "continue the case and get a default ruling" might mean.
Generally, what happens when parties to a civil case mediate and settle as a result of the mediation is that one side or the other (or possibly the mediator) will prepare a settlement agreement. Most often, the crux of that agreement will be that one party will pay the other some amount of money and the litigation will be dismissed. Depending on how long the parties anticipate the settlement to take, they may informed the court that a settlement was reached and that a dismissal will be filed within X days. However, they do not typically inform the court of the terms of the settlement. Then, once the money has been paid, the parties' attorneys will file the appropriate dismissal documentation. Obviously, more complex settlements may require more things to be done procedurally. In particular, if the settlement includes some sort of injunction, then court involvement may be necessary. Similarly, if the settlement is between the plaintiff and one of multiple tortfeasors, it may be necessary for the court to confirm the settlement as a good faith settlement (see, e.g., Cal. Code of Civil Proc. section 877.6). Of course, if a settlement agreement is breached, it may be necessary to file it with the court for purposes of enforcement. All of these exceptions are relatively uncommon.
I take it, by the way, that this means that your prior, unequivocal statement that "A judge is going to have to sign off on it" was something you simply made up.

