Is bench pressing safe/okay for a person with degenerative discs?

DDD: Benchpress and other exercises with your back supported are generally well tolerated even with the generative disc disease as long as you keep the weight reasonable. Axial type compression exercises on the other hand should be avoided such as military press.

To an extent: I assume the degenerative disc disease is in your spine (cervica/thoracic/lumbar) in that case, bench press should be fine as long as you are lifting reasonable weights (not too heavy). On the other hand, doing dead lifts may aggravate back pain.

Usually: If the degeneration is not severe, and if the workout can be done without causing back pain or neurologic symptoms, then a workout that strengthens the core can actually help delay deterioration and support the back/spine.