Do I have to dig the wire skirt into the ground or can I just sit it perpendicular to the runs with soil on top?
Digging is not required.
You can secure it to the bottom of your framing then pin the outside edge down with heavy duty landscape staples and cover it lightly with soil so grass can grow through it.
If I had mine to do over again I would use vinyl coated 1/2" hardware cloth as the contact with the soil over the years is permitting it to corrode and break. I will be covering over the old apron with a new layer of vinyl coated hardware cloth or 2x4 fencing to reinforce it this summer.
