Someone or something has stolen my bearded iris roots

Oh I hope they have not been nicked by a human 
But rabbit and mice will eat them and drag them away for their young.  Possibly, the cause can be that they have been getting very wet in the recent weather, this will rot them out, and you will likely find no trace, they just disintegrate.  Have you had a surfeit of rain at that spot or perhaps an overflowing water butt or pipe.  regards, Mrs Bouquet

Sounds like a 2 legged digger. Put up a sign saying that you were growing them & to keep their mitts off

I must admit I think so too snowdrops. It's the way it was done quite neatly , no sign of fur, pawprints etc.