if it's thin enough you can put tape on the other side of it.
I have also heard of cutting a piece of waxed paper the same size / width of your ribbon and attaching the waxed paper to the ribbon with double sided tape. That way, the waxed paper is what is up against the cake so you shouldn't get any grease on your ribbon.
or try rubbing the backside of the ribbon with crisco, so the color is uniform rather than blotchy. it will darken the ribbon abit so make sure you consider that if you are matching ribbon to wedding colors.
or...? ....place it on once the bc is dry? i think it depends on your icing recipe. for fondant, you wont need to worry about it.
try a small sample cake, or cupcake or maybe just place a thick smear of your exact frosting recipe the next time you make a batch and stick the exact ribbon you will use on it....and leave it for a day or two and make note of what happens. i'd try it with a greased ribbon and a non greased ribbon piece. as well as the same two ribbons on a smear of dry bc and fresh bc.
I agree with Melisa - I actually did a birthday cake with ribbon on it - check my photos - and it was the first time using ribbon on cake and the night before decorating the cake, I just put a thin coat of Crisco on the back of the ribbon so it would absorb all of the crisco at the same time and not have any spots. Good luck!! 
I put clear Contact on the back of mine and it works great, especially for wider ribbon.
~luraleigh~
I just read on here a couple weeks ago that someone IRONED their ribbon with wax paper...the wax adhered to the ribbon and didn't affect the color at all. Man, I wished I could remember who said that...but my mind is like the abyss!!
Try that and see...iron the ribbon between wax paper.
Quote by @%username% on %date%
%body%