Did you ever receive any therapy (rehab or medicine based) for the mild disc bulges? Do you recall the size of the bulges? There really isn’t much that can be done directly for the arthritis, but fish oils, glucosamine chondroitin, and other supplements may help alleviate the symptoms associated with the arthritis.
I still recommend finding a good movement screening specialist to determine any and all pathologies in your movement patterns and muscular imbalances present. Then you can address your specific needs, which should greatly decrease low back pain. Also, if the movement specialist has performance/strength coach background, having your technique/form evaluated on lifts that require lumbar stability (squats, deads, etc) would be extremely helpful as well.
A generic answer for your situation of low back pain with your history and without doing an in person evaluation, I would say to avoid sit-ups/crunches and any other movement that encourages lumbar spinal flexion. I would definitely not avoid lifts like squats, deadlifts, etc., but instead avoid performing squats, deadlifts, etc with improper form.
As long as you do not have any underlying pathology or current neurological symptoms from the discs, you should be fine to perform squats. If you lack proper lumbar stability, you will need to address that before going into heavy back squats and deads, but that is no excuse to completely throw out the exercises all together. You can start with single leg variations, Goblet squats, etc while working on ankle/hip/thoracic mobility drills and lumbar stability exercises.
Again though, I would highly recommend seeking out a qualified movement specialist and performance/strength coach to find specific imbalances and guide you in the right direction. If you give your location, there hopefully should be at least one person on this board who can recommend a person in your area.
If you are in the mind-frame of “doing it yourself” and refuse or can’t find a professional in your area, the “Assess and Correct” DVD is a great start, as well as the “Show and Go” exercise program.