Does a bulging disc / minor herniation repair itself over time?

Yes. Many can get better with time and conservative care within 6-8 weeks. Check out Spine-health.com.
Bulging discs are . normal findings on imaging and 90% of all disc herniations can be managed non op with relief of symptoms. Risk of recurrent symptoms range from 5-13%. By not smoking, exercising regularly and staying trim you can reduce your risk of symptomatic disc problems.
Yes. Many disk bulges will slip back in place. Gentle physical activity and protection from a repeated injury (such as heavy lifting) can help. Larger disk slippage requires a physical exam and possible additional testing to ensure complete recovery.