Mind you this is just a wild idea I had. I know that seedling pines are often shipped bare root with a very fine (read ground up) version of the water crystal polymer on the roots. I think it is made into a thick goo and the roots are just dipped in it. I can only guess that they are wrapped in plastic to keep damp and shipped that way. You could try it by packing some plants as you would for shipping and leave them whatever number of days they would be in package, but would have to be in heat, etc. Whatever you think they would encounter during shipping...see what happens.

It may be the heat rather than drying out. Do they arrive dry or with mold and mildew? If it's mold, etc., you might try soaking the paper in baking soda water. I think you need to run some tests on packaged plants without shipping them. I know that privets are tough as nails, but I suspect that the heat is either cooking them or they are being attacked by mold. Nurseries used to ship bare root plants with damp excelsior (thin wood shreds) packed around the roots. I think the idea may have been to keep damp, but also to hold some air around them. Damp sphagnum moss might work also. Hydrogen Peroxide in the water might retard mold/mildew growth, also. You might post a question about how to use/mix it on one of the organic growing forums. I'm still thinking, but it may not be worth much.

Joxo,
Not meaning to get into your business but why would someone in zone 9, California waste his time with privet? You have the opportunity to grow so many great plants that those of us in colder zones could never overwinter. Privet is the commonest of the common hedge plants. It is often given away as a bonus plant by garden catalogues if you but $25 or more.
Not sure why you posted a shipping query on the propagation forum. NO reputable nursery ever ships bareroot trees/shrubs after they have leafed out. Many of the best mailorder nurseries have stopped all shipments until Fall whether bareroot or not. Today is the first day of Summer, don't you think that the plants will cook during shipment?
Sam

I hope you are responsible enough to have these plants inspected if you are shipping them out of state.

Thanks for all the advice, and yes I make sure to get them checked.