The Court of Appeal for Bermuda has recently answered this question in the negative, in the case of Kijon Baker v The Queen  CA Bda 30 Crim, in a judgment published on 23 February 2017.
The Appellant argued, as one of the grounds of appeal against his conviction, that the trial judge, Mr. Justice Greaves, was apparently biased against him, since the judge had some level of “personal animosity” against his defence counsel, Ms. Elizabeth Christopher.
The Court of Appeal rejected this ground of appeal.
As the Court of Appeal summarized matters in its judgment: “[Counsel for the Appellant] sought to rely on exchanges between the judge and Ms. Christopher in other criminal trials and extracts from the transcript in the present case. We find no assistance whatsoever in examining exchanges between the judge and counsel in other trials. As for the present trial, there are two very important factors. First, the alleged animosity is directed towards Ms. Christopher and not the Appellant. Secondly, all the exchanges of which complaint is made took place in the absence of the jury. In our judgment, looking at the circumstances that might have a bearing on the suggestion of bias, it is critical to look and see whether the judge did or said anything that might have had a bearing on the fairness of the trial.”
In reviewing the various exchanges between the judge and counsel, the Court of Appeal noted that “Ms. Christopher is a forceful and determined advocate. Greaves J. is a strong judge who keeps a firm grip on the running of his court. Clashes have on occasion occurred between them, but there is nothing to suggest these were in any way causative of unfairness to the Appellant“.
It would be fascinating to know the details of all of the various exchanges between Mr. Justice Greaves and Ms. Christopher. Prospective clients, at least, might want to know about them!