Found This Helpful. The time it takes to recover from a biopsy depends on the type of biopsy. For fine needle aspiration biopsies, the recovery time is minimal. If the biopsy is performed under general anesthesia, the recovery time may take up to 2 weeks or more.dentify the Risks With a Biopsy. Expect to see some bruising at the biopsy site. If the bruising does not go away or start changing colors in a few days following the biopsy, notify your doctor. This may be an indication that there is prolonged bleeding from the site. Look for signs of infection.