Is carpal tunnel syndrome linked with bulging cervical discs?

No. Carapal tunnel refers to the "tunnel" through which the median nerve travels as it enters the hand at the wrist. This is a site of compression on the median nerve and is considered a focal entrapment neuropathy. Pinched nerves at the neck from bulging discs are a different location entirely.
Yes. Predisposing risk factors for carpal tunnel are diabetes, hypothyroidism, and most significantly cervical spine disease .