When treating run of the mill bacterial conjunctivitis, I was taught to use erythromycin ointment for young infants that are not yet walking, and polytrim drops for older kids. The ointment is nice in that it sticks in the eyes better, but it can be annoying to have goopy eyes for an ambulatory toddler. This is a nice summary from an ophthalmologist / comedian. In particular, as he states, stay away from gentamicin and sulfas - they often cause eye irritation. It can be hard to differentiate viral from bacterial conjunctivitis, and in the spirit of "first do no harm," you don't want to worsen the symptoms of a viral conjunctivitis that was going to self-resolve anyways.