Hi everybody!
Well, smiles, your problem started as a traumatic injury but seems that some compensations have been established that do not allow you to move without pain. I'm not sure if L4-5 bulging is the main problem, according to what you described and to the Wikipedia reference-linkMRI. You don't mention anything about narrowing of the intervertebral foramens or the spinal canal and therefore I assume that the disc does not put pressure on the nerves or the spinal cord. To my opinion, this bulging shouldn't cause symptoms, if all of the above are correct.
Assuming that the disc is not involved, then other structures should be examined, including intraarticular (eg facets) and extraarticular (muscles, fasciae etc) and not only at the lumbar spine. This must be done clinically by your physio or osteopath and I can't make any assumptions (actually I can guess but this is not the case at the moment). One thing I'm worried about is what you said about the length of your hips. If your left leg 'seems' to be shorter but in fact it's not, then it's not an anatomical abnormality but a functional compensation and you shouldn't use an orthotic device at all. A pelvic side tilt is a more possible explanation and this can be corrected. Now, if this tilt is secondary to a mild Wikipedia reference-linkscoliosis or to a tightened muscle group (the gluteus could be but again this itself could be for example due to a tightened piriformis pressing the sciatic nerve and causing you hamstring area pain) or fascia or something else, it should be assessed by the physio/osteopath.
In conclusion, I think that the cause of the problem might be at the lumbar spine but not a bulging disc. It looks like more of a bad motor control secondary to an injury. If this is true (only a clinical assessment together with your medical history could prove this or not), then proper physiotherapy scheme could alleviate your pain and restore function. I'd like to hear from you if something changes.

Regards,
ilias