What is the best way to secure fabric to a cork board?

I have a bulletin board where the cork is a little shabby looking. Being crafty and thrifty (plus having screws = holes in the wall where this one has the hangers located) I want to cover the cork with either paint or fabric. I have some nice fabric that replicates the tan look of the bulletin board cork. I was thinking of putting quilt batting under the fabric, so it looks kind of quilted. I might put a ribbon or something around the edge of the fabric so it does not look raggedy.

What is the best glue or way to fasten the fabric to the outside edges of the cork?