Certified GKH Gardening Expert
It could be a mold of some sort or could be caused by a dog or cat relieving themselves on or near the rosebush. I would dig out a sample of it and take it to a local nursery or University Soils Lab and have it examined. Ask them what course of action should be taken.
It might also be a flat type of mushroom if wet to damp conditions are present, in such case it should be dug out and destroyed so that the rosebush is not harmed.