Hi, I am sorry to hear of your pain. I know from personal experience that back disease can be debilitating.
Disc bulges are NOT uncommon. They only need to be treated if they are implicated as the cause of your symptoms. They are NOT always symptomatic.
If your only symptoms are pain and you do not have other problems like bowel or bladder issues, weakness, or progressive symptoms then it makes some sense to hold off on surgery. However, it is hard to disagree with a neurosurgeon who has the advantage of history, physical, and MRI
images and report.
I feel your best option is to get a second opinion
before completely writing off surgery. In the meantime: Consider PT, anti-inflammatories, icing alternating with warm compress (see which is better), icy/hot or ben gay, an over the counter back brace
Another option may be spine injection which should be considered prior to surgery. I agree that surgery should be reserved only if the other treatments are not working.
Best of luck, I hope you start feeling better.