Bulging disc in lower back. Right side hip pain and sciatic shooting pains down legs. Medications or non surgical treatments for relief?

USUALLY. Over 90% of bulging discs with sciatica will get better without surgery. Non-surgical treatments (PT, Chiro, etc) along with either medications (NSAIDs or short burst of oral steroids) and possibly Epidural steroid injection should take care of most.
Evaluate Low Back. If you are not improving have your doctor order a lumbar spine mri. Many times a herniated disc in the back can cause leg pain especially if you have not improved with the medications and physical therapy. If it is a herniated disc you may need evaluation from a spine specialist to determine what other options might be needed (injections, surgery, etc) to help reduce pain.