Final answer:
The sensory nerve that supplies the bulbar conjunctiva is the trigeminal nerve, specifically the ophthalmic branch. It plays a key role in initiating the corneal reflex that results in blinking, either through a tactile stimulus or bright light.
Step-by-step explanation:
The sensory nerve that supplies the bulbar conjunctiva is the trigeminal nerve (specifically the ophthalmic branch, also known as V1). In the context of the corneal reflex, or eye blink reflex, this nerve has a crucial role. When the cornea is stimulated, the sensory signal is carried through the trigeminal nerve, triggering the reflex that results in blinking. For protection, this response is also initiated through the optic nerve when bright light is used as a stimulus. The motor response is mediated through the facial nerve, activating the orbicularis oculi muscle to close the eyelid.