They will find a Judge and I don't think it is so much that the Mayor is powerful, but rather the court choosing to avoid any potential for accusations of favoritism or room for not having a fair trial.
It is not unheard of, or even perhaps a good thing that the entire bench in this court / locale file for Judicial disqualification and recuse themselves. Just like a change of venue to help ensure or give a trial a sense of fairness over the proceeding. Judicial DQ and bring in an outside Judge, will at least ensure that there is no bias, positive or negative, from the bench in the trial. It does not mean that a judge has a connection to the Mayor, but perhaps more important, for a judge that may have a positive connection with the Mayor is opting to not hear the case. This should be a good thing because it would be unethical or worse if a judge that had some kind of positive connection to the Mayor actually wanted to hear the case.
I will say that it is my feeling that the BI has one of the worst, old boy networks.