Bias will come from the training
Let's take application screening as an example. How would you train that? The easiest way would be to feed it all the applications you've had over the past however many years you have electronic records for along with which of those candidates reached further stages of interviews and which were ultimately hired.
If your hiring process was bias free then an AI trained on that historical information will be bias free. How many organizations can truly say that though? Even ones that have made efforts to be free of bias, that doesn't guarantee none of the decision makers whose decisions went into that training data had bias and weren't found out or were ignored due to their "power" in the organization. If there were enough men who tended to choose men over women when they were otherwise equal (or maybe even when they were not) the AI will inherit that bias. If candidates over 50 years old have been disproportionately screened out - something fairly common in the tech world - then the AI will do the same.
And yes, it doesn't matter if there is no direct information for the AI about "age" and "sex" provided on the information fed to the AI. It will pick up on other factors that represent that information, like whether the applicant's first name is male or female, graduation dates, years of experience, etc.
If you doubt that, refer to the example about the AI that was trained to look for cancer (I think it was) on radiology scans by being given a large corpus of previous scans of people who had and did not have cancer. They trained it, then proved how good it was by giving it other previous scans not included in its training, and it did amazingly well. It then utterly failed with new cases. Because as it turns out, the AI didn't pick up on cancer/no cancer from the radiology scans. It picked up on it based on text that was included in the margins of the scan listing the actual diagnosis of that case. People just assumed it would be looking at the scans, but it was looking at EVERYTHING it was provided and that was the information that best matched the "right answer".