Hi Frances,
Most problems beginners have with their trees are usually a combination of location and watering. It would be best to check your tree daily and water as needed than to rely on a fixed watering schedule.
Evergreen trees do shed their leaves. Usually this occurs as the new growth develops. If the rate that the new leaves are appearing keeps everything in balance, it's not a problem.
here are some notes on
Chinese privet as bonsai by Zach Smith
P.S. It would be great if you could post a picture of your bonsai.
Regards,
Matt