I'm not a doctor, but have quite a bit of exposure to these problems. What is the severity? Is it just a "bulging disc", or a full blown hernation (i.e., encroachment on the nerve root and/or spinal cord). One doctors disk herniation is another doctor's bulge. The MRI scan would answer these questions (but not always) If you actually have peripheral symptoms (i.e., Radicular Symptoms), that would suggest a true herniation.
I actually have three bulging discs in my neck, which is not all that uncommon once people hit 40 (although I am only 37). The L4-5, and L5-S1 are the most common sites for disc problems. Apart from DCS, I can't imagine slinging on a weighted BC and tank if you are symptomatic. Maybe you could put it on in the water, but if it's a true herniation with symptoms, there is no way I would.