Surgery to remove the bone spurs takes the compressive forces off the spinal cord. This treatment relieves symptoms and stabilizes the spine. Since this was the common belief, surgeons weren't willing to withhold surgery in order to compare results with and without the operation.
Over the years, patients who didn't want surgery could be compared to those who had the operation. Results showed that a significant number of patients not only didn't get worse with conservative care, they actually got better! Conservative care ranged from bedrest to activity modification to wearing a collar of some type. Physical therapy and psychologic support have also been successful treatments.
It's probably best to pursue nonoperative care under the supervision and management of your doctor. Follow-up X-rays and MRIs will help make sure you aren't in any danger of disability or even death, which is possible with this condition.
Even mild CSM requires careful watching. Expect to remain under your doctor's care for years or until you stabilize. This is one of those situations when it's better to be safe than sorry.