Final answer:
Genital herpes is the sexually transmitted disease that is not caused by a bacterial infection. It is caused by the herpes simplex virus (HSV) and cannot be cured with antibiotics.
Step-by-step explanation:
The sexually transmitted disease that is not caused by a bacterial infection is genital herpes. Genital herpes is caused by the herpes simplex virus (HSV), specifically HSV-2. Unlike bacterial STIs such as gonorrhea, chlamydia, and syphilis, genital herpes is caused by a viral infection and cannot be cured with antibiotics.