<tongueincheek>Well I also don't really want them tearing up any more of the vegetation than they have to. I was hoping if I made them a place to dust bathe, they'd use it more. As I said, I don't really have a lot of just dirt... it's grass. Plus, under the grass is lovely clay.
Yeah, well, you can hope.....eventually all the vegetation in run will be gone...how soon that will happen depends on how big a space and how many birds.
Or maybe you free range....... then they will probably dig ankle breaking holes exactly where you don't want them to.
They are particularly attracted to freshly planted, carefully mulched flower beds.
I've lovingly prepared several dust bathing areas, they ignored them all and dig their own......
......with the exception of the bin of sand and dirt I put in the coop for winter when everything outside is frozen solid, they use it some but not much.
If your ground is truly solid clay, you might try dumping a bag of sand somewhere, they might appreciate it.
Otherwise play it by eye, see where they choose, time will tell.