If you have a bulging disc, you should stay away from any motion that would put you into a lumbar flexion (assuming a posterio-lateral bulge-which is the most commong direction). This would include any leg press or hack squat (machine based). Those devices take you out of a proprioceptive rich environment and place you at greater risk of reproducing the movement patterns that exacerbate your condition, namely spinal flexion.
You’d want to first learn how to find, hold and maintain neutral spine and work on specific lumbar spine stabilization exercises (planks, birddogs etc) which activate the necessary musculature but decrease the spinal loading component. bodyweight movements are a good start (consider single leg) which would also work on hip range of motion. Many times, lumbar compensation takes place due to lack of hip mobility (e.g. lumbar spine “hitching”).
Start slow and progress slowly. Nothing should be painful. Think of it as retraining your body how to move by NOT using your back.
Once again, I would stay away from leg press, hack squat or other spinal loading machines. As well, stay away from any abdominal work that puts you in to a flexion position (curl ups, crunches, twists, rotations). Not worth the loading that takes place through the discs and vertebrae.