“Does bacterial conjunctivitis go away on its own?”

Generally bacterial infections need to be treated with antibiotic eye drops to clear up. Viral infection usually clear on their own with just palliative treatment or artificial tears . It is hard to differentiate bacterial from viral infections without seeing an Eyecare provider

Can but takes weeks and very contagious

Yes, eventually your body’s natural defenses will beat it unless it is a super bug. You can be left with chronic redness and scarring depending on the severity. Most people are fine with simple cases, but if it is very painful, oozing green puss that you wipe away and it comes back almost immediately, or if the eye is swelling or painful on eye movements, you should see your eye doctor right away. Otherwise washing your face frequently and putting in artificial tears to decrease the bacterial load will help your body fight off the infection. Good ole Vitamin C is always good to take too.

Sometimes if the infection is mild

No it needs treatment .