My girlfriend had a CT scan that revealed a "small vesicovaginal fistula". Should a urologist perform the repair surgery or a gynecologist?

Urogynecologists. You would want to talk to someone who specializes in urogynecology, which can be either a gynecologist or a urologist. Both will have done further fellowship training in issues specifically related to fistulas like your girlfriend has. I think more obgyns are going into this area, at least where i am, but look at what is available in your area.
Expert urologist. Causes of vv fistula r prolonged childbirth usually due to poor or no obstetric care, congenital problem, or surgical complication. Sugery is fairly complex & requires an expert urologic surgeon with experience in this field. Bladder needs 2b closed correctly in at least 2 layers & requires interposition of momentum between bladder & vagina. Expertise usually found in & advise major urology center.
An expert. Make sure you get an expert in fistula repairs. Do your research.
Both. A surgeon with experience should perform the repair, and have colleague(s) from the other speciality consult on the case, available during the surgery, and possibly assist in the procedure. One surgeon must be the lead, but it should be a team effort.