A Ligustrum, also known as Chinese Privet, which has been inside should never be put outside in the winter without going through the gradual cooling of fall weather. Give it lots of light but not direct afternoon sun.
Ligustrum are very tolerant of both full sun in the summer and deep shade. They are cold hardy and can handle temperatures in the 20s but should be brought inside if it gets below 20° F. The colder the temperatures a Ligustrum are exposed to, the more leaves they drop.
This is a natural reaction and causes no permanent damage even when specimens lose all their leaves in severe cold. New growth comes back quickly in the spring. Ligustrum that are left outside during the winter must have spent the autumn outside in-order to acclimatize to the cold.
Bonsai trees live in small pots and their world dries out much quicker than plants in the ground or in bigger pots, so close attention should be paid to watering. Check and water your bonsai every day. Striking a balance between not enough water and too much water can be a bit tricky but is very important. Give it enough water to keep it from drying out and remaining dry. A Ligustrum will tolerate over watering well and will wilt if it gets too dry for too long.
Water thoroughly and deeply when it needs water and let it catch its breath before watering again. An old bonsai watering trick is to place the entire pot in a sink of water an inch or two deep and let the water absorb from the holes in the bottom of the pot. Another favorite way to know if it needs watering is to lift it. You can get a sense for whether it needs watering by its weight.
An inexpensive moisture meter takes the guesswork out of watering.