“Can I workout with a bulging disc?”

Try Pilates

Yes, but I would recommend that you avoid exercises that could exacerbate, or worsen, your symptoms and put undue strain on your back (and injured disc). This would include impact activities, bending and lifting, and twisting. It is however important to perform exercises, either self-directed or under the supervision of a physical therapist, to improve your range of motion. Paradoxically, activity is better than inactivity after a lower back injury!