What is the best way to handle a situation where I believe a moderator is biased?
If a moderator is the problem, who moderates the moderator?
If there is actually a moderator that is as biased as you claim, there should be individual moderator actions that are problematic. You can bring those actions to meta and see if the community agrees with you that they were incorrect.
There is one extremely important aspect when bringing the issue up here on meta, and that is to make it about the individual decisions, not about the moderator as a person. Your meta post shouldn't even mention the name of the moderator acting, just the post and the facts. This kind of issue is handled far, far better if everyone stays close to the facts and avoids making the issue personal.
A reasonable moderator will change their behaviour if they are convinced that some of their past actions were incorrect. Often such disagreements simply indicate an area where the commmunity hasn't come to a consensus on the rules, and a meta discussion can solve this by coming up with better rules.
If a moderator is continuing to misuse their position in your view, use the "contact us" link in the footer. The complaints about moderators will be handled by the SE commmunity team. They moderate the moderators, and can talk to them or in the worst case also dismiss them.