Water the privet bush two days prior to transplanting it so the soil is moist and pliable. Provide a steady stream of water to soak the root zone completely.
Cut the bush back to two-thirds its size with sharp, sterilized pruning shears or loppers. Reducing the weight of the shrub not only makes it easier to transplant, it also helps the plant recover when there are fewer roots to support growth during the season. If desired, wrap rope or a soft cord all the way around the foliage to compress its branches so it is easier to move.
Insert the tip of a shovel into the ground, 24 to 30 inches from the base of the bush, and begin digging down to break the soil, forming a 10-inch-deep and 6-inch-wide trench all around. Collect the soil in mounds nearby, exposing as many roots as possible. Avoid damaging the roots during the digging process.
Slide the tip of the shovel under the roots, along the edges of the root ball. Apply force on the shovel to remove any residual dirt and loosen the roots. Start from one end of the trench and work your way all around the bush, back to the starting point, freeing up roots all the way along.
Grasp the end of the privet bush and rock it back and forth so it loosens up and moves freely in the soil. Gently tug the bush so it slides out of the planting hole. Lay the bush on its side just outside its old planting location and remove any large clumps of dirt attached to its roots by hand.
Moisten the roots to keep them from drying out while you transport the bush in a wheelbarrow or on a tarp to its new planting site in your yard. Ensure the new hole is twice the width of the root ball but equally deep. Plant the privet at the same height as its previous location. Spread 2 inches of organic mulch around the base of the privet to retain soil moisture.