Q.How to prepare a basil shrub for winter
This is not the edible plant. This one grows 3 feet and has beautiful purple flowers

Certified GKH Gardening Expert
You did not mention whether your shrub is containerized or planted outside. If it's potted, it should be moved to a garage or basement to protect it from the harsh cold of winter. If it's in the ground, you may want to mulch generously around the base, and wrap it loosely with burlap. Here's a helpful article for you:
https://www.gardeningknowhow.com/plant-problems/environmental/protecting-plants-winter.htm