Here is a complete, evidence-based answer on antibiotics for bacterial white discharge (Bacterial Vaginosis - BV):
Bacterial vaginosis (BV) is the most common cause of white/gray vaginal discharge. It results from a shift in normal vaginal flora - lactobacilli are replaced by polymicrobial gram-negative anaerobes (mainly Gardnerella vaginalis, Mobiluncus, Bacteroides spp.).
Metronidazole oral and clindamycin intravaginal cream have equivalent efficacy (Cochrane review, 2009). Clindamycin cream has fewer side effects.
Note: This is for bacterial vaginosis specifically. If the discharge is thick/curd-like with itching (candidiasis), antifungals are needed instead. If there is a sexually transmitted infection (chlamydia, gonorrhea), different antibiotics apply. Please confirm the diagnosis before starting treatment.