The so-called AI parses your resume looking for keywords that match the job description. They anonymize and provide a summary. I don't think there is much room for bias. Maybe if you use crappie software that doesn't make the summary anonymous.
BTW write your resume for the algorithm not the manager.
AI resume screeners are very much at risk of bias. There have been stories about exactly this in years past. The ML models need to be trained, so they get fed resumes of candidates that were hired and not hired so the model can learn to differentiate the two and make decisions on new resumes in the future. That training, though, takes any bias that went into previous decisions and brings it forward.
From the Amazon I linked above, the model was prioritizing white men over women and people of color. When you think back to how these models were trained, though, that's exactly what you'd expect to happen. No one was intentionally introducing bias to the AI process, but software teams have historically been very male and white, and when referrals and references come into play, those demographics were further emphasized. And then let's not pretend that none of those recruiters or hiring managers were bringing their own bias to the table.
If you feed that into your model as it's training data, of course the model is going to continue to favor white men, not because it's actually looking for men, but because resumes that men typically submit are the kinds that get hired. Then they found that resumes that mention a professional women's organization or historically black or women only colleges were typically not hired. The model isn't "thinking" about why that is - it just knows that when certain traits exist, the resume is ranked lower, so it replicates that.
It depends how “bias” has been defined. The Ibram Kendi definition is unequal outcomes. Since no two groups are identical, such definitions require bias to be “unbiased.” Australia tried to employ blind recruitment and hired fewer women and minorities. That’s true unbiased recruitment, but I suspect it wouldn’t be praised today.