Last week I noticed this new growth on my bush orchid. At least, that is what I have believed this orchid to be called. This morning in my searching I have found this site, which actually calls it a "rock orchid".
I was uncertain as to what this this new growth actually was until I read this page. It appears that it is new roots, and that they will be looking for food. So this means that I have to either re-pot this orchid, or divide it up. Something I will have to look into doing very shortly.