Herniated discs in the low back (especially L4,L5 and S1)) don’t always cause pain, but when they do, irritation of the nerve root 
affects all of the muscles along the sciatic pathway. With medical sources ruled out in the spine and disc , the pain is most likely caused by muscles.
When butt and leg pain are caused by a herniated disc, a Neuromuscular Therapist looks for four primary causes: A structural asymmetry, entrapment of nerves and blood vessels, Trigger Points and local soft tissue irritation.
A. When symptoms are one-sided, my Neuromuscular Therapy training has taught me to suspect a structural asymmetry, a commonly overlooked imbalance in the two sides of the body. Muscles get tired from trying to create balance. They keep working and get tuckered out and energy starved from trying. Then they start crying for help. Something as simple and inexpensive as a heel lift can solve the problem with proper muscle therapy, stretching and exercise to strengthen the core muscles.
B. As a Neuromuscular Therapist, of course I am interested in what muscles have Trigger Points that refer down the leg. They may be different in each case, but the following muscles are the major causes:
The source closest to the spine is a little muscle deep in the small of the back called the quadratus lumborum. With uneven legs, this is usually the culprit. - The second is the piriformis. The sciatic nerve exits the pelvis under this little muscle and when it is bulked up in a contracture it can press on the nerve and produce a loss of sensation and function all the way down to the foot.
Entrapment! The combination of factors from what is now better known as Piriformis Syndrome were hardly recognized 18 years ago. The piriformis muscle also has Trigger Points that refer into the butt and down the back of the thigh. 
The third common source is another little muscle in the side of the hip called the gluteus minimus. It’s referral patterns exactly mimic “sciatica.”
C. In Neuromuscular Therapy one of the major things we look for is signs of “neurovascular entrapment” when nerves and blood vessels are trapped. I am always concerned when foot drop and numbness occur. Numbness is never a good sign and foot drop means that a nerve signal is not getting to the foot. Entrapment! Two major locations are Neuromuscular Therapy targets, the piriformis and the peroneus longus in the lower leg.
D. Leg pain caused by irritation from Trigger Points higher up in the back or butt is common. Those local symptoms need treatment to “centralize” the pain, meaning to eliminate the pain farthest away from the source and work your way back.