The reason for using bias tape on the armholes is that the bias tape will mold itself to the curve nicely. Ribbon is normally somewhat stiff and likely to be scratchy where it bunches up (which it probably will) going around the curve of the armhole.
Using the ribbon as a bit of trim on dress would be a lovely touch, but for binding the armholes, I would use bias tape, either purchased or 'make your own'. I've seen a tutorial listed on this board for how to do that. Sorry I don't know how to do a link, but I'm sure you can do a search and find it.