I know nothing about privet, specifically, but as you probably know, various woods can be made in to bows for various reasons and it is up to us to learn how to handle them. Some may be more flexible, some stiffer but still elastic, some very elastic but not very hard, etc.
So Pat mentioned Chinese privet is a TOUGH wood. I doubt it is as tough as osage because it isn't as dense or hard. But TOUGH is a good place to start. Tough, but lighterweight woods like hickory, pecans, elms, etc. are good for bows because they just don't want to break. Baker said in the TBB's, that a bow is a bow until it's back breaks, so the rest of the task is just to find designs and construction methods suited to the other strengths and weaknesses of that wood.
For instance, in my experience, elm likes to be made into longish flatbows with high crowns and flat bellies, from smallish diameter young trees grown in thickets, maybe with slightly flipped tips or even recurves from a stouter, shorter tree, if say it won't give you a 68" stave.) I have worse luck witn elm wood from larger trunks, but that may be due to variety of elm available locally.
So, it sounds to me like if you have plenty of privet available, you should easily be able to find something to do with it.
Good luck!
