A prostate biopsy can inject bacteria into the prostate itself and possibly spread cancer cells to a location they hadn't occupied previously?

Yes and no: Prostate biopsy is a surgical procedure and any such procedure carries the risk of bacterial infection. There is, however, no evidence that the procedure will spread cancer to other areas of the prostate or elsewhere in the body. Unfortunately, this a widely held belief that prevents many patients from receiving needed treatment. Talk to your doc if you have further questions.

Unlikely: While the biopsy can cause infection, this doesn't happen very often. Many biopsies are performed to evaluate the prostate by urologists. The tumor is not known to spread along the needle track.