For what length of time can bacteria remain in the eyes?

Unclear question: Normally, bacteria are not present within the eye. If you are referring to the surface of the eye, we all have resident bacteria there. If you mean a specific bacterial eye infection, that is something that will likely not resolve on it's own and needs treatment.

Not long: The eye is assaulted with bacteria all day as long as you are walking around with the eyes open. The surface barriers and tears are excellent at fighting them off and so bacterial infection in the healthy is rare. You also have some bacteria that always live in the skin and actually are part of your defenses since they ward off more dangerous bacteria.