What is the recommended non-surgical way to alleviate lower back pain associated with bulging discs in the l4/l5/s1?

Acute? Chronic? Anti-inflammatory medication in combination with muscle relaxants and physical therapy for the first 3 months, possible epidural steroid injections if your pain persists beyond three months.
Several things. Pain medications such as non-steroidals or a course of steroid medication, heat, injections into the area may all be helpful. Improve your posture. There are some exercizes popularized by robin mckenzie which i found very helpful. A "lumbar roll, can be used to support the back when sitting or sleeping and will help improve poor posture.