Final answer:
The assistive personnel (AP) should wear a mask to prevent the spread of bacterial meningitis, a highly contagious infection.
Step-by-step explanation:
The nurse should instruct the assistive personnel (AP) to wear a mask when caring for a client with bacterial meningitis. Bacterial meningitis is a highly contagious infection and can be spread through respiratory droplets. Therefore, wearing a mask is crucial for infection control. Wearing a gown, keeping the room well lit, and maintaining the head of the bed at a 45 degree angle are not specifically related to preventing the spread of infection.