I think that it depends on which way the disc is bulging. Usually they bulge out toward the side/back, but if a disc bulges inward toward the spinal cord, it can impinge on the cord itself. That can potentially cause symptoms lower down than the Brachial plexus dermatome, and/or could be of a different nature because the pressure is on the cord/dura rather than on the nerve roots that just supply the upper extremity.

MS can affect the central nervous system & lower motor neurons that are within the spinal cord, so the symptoms may not follow peripheral nerve distributions.

Having both MS and bulging discs can produce CNS and peripheral nerve symptoms at the same time, which can be confusing, even to the experts; as it is often difficult to figure out the exact cause of the symptoms. A lesion within the spinal cord would make that differential diagnosis all the more difficult.

Hoping that you get relief soon .

With love, Erika