Is a breast biopsy safe when i’m pregnant? I’m 12 weeks pregnant and i’m worried the anesthetic could be bad for my baby?

Yes. A core needle biopsy can be performed safely with local anesthesia in a doctors office.
Yes, it is safe. The biggest error would be to avoid biopsy of a suspicious mass in a pregnant patient. Local anesthesia should not put the fetus at risk. A surgical biopsy should alway be avoided, if at all possible. General anesthesia and IV sedation should not be used during the first trimester.
Yes it is safe. You need to let your anesthesiologist know about your pregnancy, but there are anesthetics that are very safe during this period. The surgery itself is minimal and can be done under local and light sedation.