Given that this is an own root plant and it is apparently growing from the roots of your established plant, this is most likely a rootlet of a new baby Bliss. Congratulations, you're now a new grandparent :)

If you want to divide the plant once it's well established and plant it elsewhere, that is a way some roses propagate themselves. Sometimes you can deliberately try to get a rose to make new "mini-me" plants by drawing a cane close to the ground to get it to root itself (this is called "pegging"). Some roses take to it and some don't, but it can be fun to try. Technically if the rose is still patented this is propagating the rose and not something to be shared with others because it's still licensed for the royalties to the breeders. I don't usually deliberately propagate patented roses in my yard but if they decide to do so by themselves who's to stop them?

Obviously if this were a grafted rose, you'd have to check that the sprout is coming from above the graft (a "basal break" and the desired rose) vs below the graft (the rootstock and not the desired rose). If you see the rootstock growing on a grafted rose, you should rip it off the base rather than cutting it, so that you kill off that connection rather than just delay it.

Yours looks like a great "lucky break" in a new mini plant of Bliss. It's a wonderful and hardy survivor of a rose so I'm not surprised it's branching out.

Cynthia

I had a monster Lillian Austin that was my favorite of all my roses. One day I noticed that it had RRD & I was heart broken. I started chopping it down & during the process of getting it out I noticed a shoot from a root that looked just like yours. My DH pulled out the rootball of the original rose & left the root with the new shoot. Within a couple of years I had a decent size Lillian Austin with no RRD. I was so thrilled!!!

Yayat!! a new baby Bliss I have gotten 2 babies from Soul Sister. I just love those new babies.