I'll assume the quantity you're looking at sending is smaller than say a box of a dozen wine bottles, perhaps with an end goal to help people start their own worm farm.
If an unexpected delay in shipping or other unexpected circumstances caused the package to start to leak, you may find that you're liable for any damage caused. To avoid such leakages, the outer layer of the packaging should be largely watertight, and some absorbent material underneath that layer would help soak up any minor seepage.
I suggest wrapping the vermicompost in non-glossy newspaper (without squashing it too much, as you don't want it to decay anaerobically), then padding it with a layer of scrunched newspaper to allow air to be retained within the packaging. A layer of (biodegradable preferably) plastic to avoid leakage around that will help prevent spills.
Depending on how rough your shipping business is, and how leaky the vermicompost can be, and your tolerance for risk, another layer of newspaper and another layer of plastic may be needed to be sure you can avoid problems.