If it's a fine needle aspiration then both times I've been for my first appointment (two separate occasions) they did it then and there. The first one the surgeon did after examining me, before my scan, and the second one the radiologist did while she was doing an ultrasound.
I only ever had one appointment. The first time I rang for the results a few days later I think, the second one they said to wait and I got them on the same day.
Both harmless fibroadenomas (did I get it right this time sqad? ;)).