I keep my mulch 4-6" away from the rose stems (in z4 my bud union is buried) & I try to put on 2-3" at a time. You say that your mulch is "fine", most info I've seen recommends something courser like wood chips to allow rain/water to run thru. I use wood chips that I can get "free for the hauling" at a site run by my city gov't where they haul their tree trimmings. I am a big advocate of using local mulch like this rather than buying it, think "mulch locally" just like you frequently hear "eat locally". Below is a link to some good articles to read on mulching.

Here is a link that might be useful: Hort. Myths