Goats will generally drop the alfalfa stems on the ground, and this becomes the bedding in the barn. We clean ours out every six months or every year and use it for making
compost. Goats will eat more stems if the alfalfa is finer, which is usually true of the later cuttings. At a feed store in late summer you can find later cuttings. I haven't generally seen organic alfalfa available, though.
You can also get alfalfa pellets. In that case they won't have a choice to drop the stems. But then you have to provide some other bedding material. To us it seems easier to let the waste alfalfa be the bedding material.