Final answer:
The N-95 respirator provides the best protection for a phlebotomist when drawing blood from a patient with active TB.
Step-by-step explanation:
The best protection for a phlebotomist when drawing blood from a patient with active TB is an N-95 respirator. TB is primarily transmitted through the air, and an N-95 respirator is designed to filter out airborne particles, including the bacteria that causes TB. The other options, such as double gloves, surgical mask, and shoe covers, do not provide adequate protection against airborne particles.