I also transplanted a rose. Beautiful Marie Pavie has always been quite beautiful along the fence on the north side of the property. However, things change. You can see how it looked a few years ago in the link but the past few years, she has suffered from less sunlight and crowding from the evergreens planted nearby. I decided to move her to the front border outside the fence in front of the house.
When transplanting, dig as much of the rootball up as you can and try to keep it intact. If the rootball crumbles and falls apart (which often happens), just mound a cone of soil in the planting hole and spread the roots down over it, like you would when planting a bareroot rose.
Dig your hole in advance and add some compost or good soil to the planting hole. When digging the hole, keep in mind that the width is more important than the depth. Rose roots spread outward and don't go that deep.
Place the rose in the planting hole at the same depth that it was growing in its previous home.
Fill the hole with soil and water it well. Gently tamp down the soil to eliminate air pockets. Apply a generous mulch -
Finally, prune the rose. As you can see here, I pruned this one pretty drastically. I cut out all the dead canes and cut the green canes down to an outward facing bud. (If you are transplanting a large and unruly rose, you might want to prune it first before digging it up.)
In a few weeks, when new growth appears, I will fertilize it lightly. Hopefully, she will be beautiful again in her new home.