What are the chances of a bulging disc becoming a herniated disc?

Possible!: Discs undergo changes with age, like car tire wears with time. Disc degenerative start with dehydration of the nucleus pulposus which results in low disc turgor. Hence the disc height decreases, and "bulges" -- like tire with low pressure. This leads to more stress on the annulus covering which then tear, and disc can then herniate from tear. Like driving on a flat tire, exposes the inner wires.