Will exercise help a bulging lumbar disc?

Yes. Bulging discs are seen in normal individuals. A routine exercise program can help with lower back pain. See your physician before starting any new exercise program.
Low impact. The best exercises for a bulging disc are low impact. You want to avoid axially loading the spine and increasing pressure on the disk. Water exercises such as swimming, stationary biking, or walking are safe. If symptoms increase, back off the exercises and see your physician to ensure that indeed it is a bulge and not a disc herniation.