I didn't bury mine. I got 2' wide wire, and made an apron around the run. I then went back and pegged it all down with metal tent stakes. Then, DH put some dirt down over the top of the wire to help discourage digging. This is much easier than digging down a couple feet to bury the wire.
I'm with you, henless. We pinned our 2' hardware cloth apron down with landscaping pins and mulched over it. There's just not much fun to be had in digging out clay soil to any depth. We're thinking about planting some chicken friendly stuff around the coop / run when planting season returns in mid-May.
I did aprons over the grass too......in some places it worked ok but I wish I had buried it at least a couple inches as it is not staying staked down and the mower blades tear the heck out of it.