If there were no extenuating circumstances (or they should not have been looked at as they were not presented), the losing party can petition for reconsideration and appeal the decision as a matter of law. The Judge/court of appeals then reviews the case and decides if the verdict stands. But you can't plead new facts at that stage, so if the losing side's lawyer messed up the case, that's up to them, not the judge. If it was a criminal case, the victim can't force the DA to appeal either, though they can try to get an injunction in related civil cases.
But no person, or for the matter neither party, can sue the judge at all for misbehavior on the bench because judges have judicial immunity. Even when they did something so out of scope, such as a judge ordering from the bench that a lawyer shall be beaten up by police because they missed a court date, they get immunity as they acted as a judge (Miles v Waco). Indeed, let me quote from the first section of that SCOTUS case (emphasis mine):
A long line of this Court's precedents acknowledges that, generally, a judge is immune from a suit for money damages. See, e. g., Forrester v. White, 484 U.S. 219 (1988); Cleavinger v. Saxner, 474 U.S. 193 (1985); Dennis v. Sparks, 449 U.S. 24 (1980); Supreme Court of Va. v. Consumers Union of United States, Inc., 446 U.S. 719 (1980); Butz v. Economou, 438 U.S. 478 (1978); Stump v. Sparkman, 435 U.S. 349 (1978); Pierson *10 v. Ray, 386 U.S. 547 (1967).1 Although unfairness and injustice to a litigant may result on occasion, "it is a general principle of the highest importance to the proper administration of justice that a judicial officer, in exercising the authority vested in him, shall be free to act upon his own convictions, without apprehension of personal consequences to himself." Bradley v. Fisher, 13 Wall. 335, 347 (1872).
Like other forms of official immunity, judicial immunity is an immunity from suit, not just from ultimate assessment of damages. Mitchell v. Forsyth, 472 U.S. 511, 526 (1985). Accordingly, judicial immunity is not overcome by allegations of bad faith or malice, the existence of which ordinarily cannot be resolved without engaging in discovery and eventual trial. Pierson v. Ray, 386 U. S., at 554 ("[I]mmunity applies even when the judge is accused of acting maliciously and corruptly"). See also Harlow v. Fitzgerald, 457 U.S. 800, 815-819 (1982) (allegations of malice are insufficient to overcome qualified immunity).
In the example OP posed nobody, not even the police, becomes liable for the actions of Bob but Bob himself: Police does not need to help you, even if they know for a fact that something is happening right now.
There's a huge error in the case as presented by OP
You start to work up a case, and points 1 to 3 are fine. But you start to get off the rails starting in point 4: The evidence does not say that someone is to be locked up, it only indicates what the facts of the case (upon which is to be decided) might be. The decision if someone is to go to jail or not is only up to the verdict - which happened in dot 5. Dot 5 however indicates that the judge looked at extenuating circumstances which is also evidence, so point 4 is presented incompletely.
Let me present a more complete version of point 4: Evidence from side A was presented, as was other evidence by side B. To the victim, it seemed that side A (either her attorney or the DA, not clear from OP) had the better evidence and might get a conviction on side B. But the Judge did weigh the evidence differently than the observer and declared a verdict favoring B in point 5 to the dissatisfaction of the victim
The missing bullet between 5 and 6 (a motion for reconsideration or appeal) does not seem to happen. Assuming it did not happen, because months go by, the verdict becomes final and the case becomes res iudicata - the case is closed.
Point 6 is a different and separate crime. The case files of the earlier case can get pulled to show a pattern of behavior, but not to re-adjudicate the earlier case.
Finally: Point 7 does not matter before the law: If-Then hypotheticals can't be adjudicated. Because the counterpoint to the presented argument in this point is: Would the lawyer of Side A have filed for reconsideration and/or appeal, the verdict would not have become final and waiting for the verdict from the court of appeals, Bob might still await the next step of the trial.
As presented, the rundown of the hypothetical case does not present anything that the judge could be liable for but instead shows that side A did not take the necessary steps to ask for reconsideration or file an appeal to the verdict they didn't like.
The separate incident opened a new case, the hypothetical that side B would sit in jail is conclusory.