I think you leave it until too late. When you dig the bush up, just make sure you have a huge plastic bag to put it in immediately. Then keep this bag in the coolest spot away from the Sun. The bag helps to keep the moisture in so the roots won't dry out.

Taking cutting is OK. Make sure you take fairly mature canes and seal into aplastic bag and keep in your fridge just like keeping veggies.

Now, the next thing you might like to venture is to graft (bud) it on another live host to make sure you have a copy. You can buy a potted rose of easy type like Iceberg or something that grow very easily. Take a bud off this rose and graft on the potted rose. This buy you time to do more later when you settle at the new place.

I just moved a Madame Alfred Carriere that is 3 years old and 6 feet tall. I first dug a 4 foot diameter circle around the rose (2 foot radius). I recut the circle every few days all the while watering the root ball. I did this for 2 weeks. Then I halved the circle to form a 2 foot diameter root ball. I recut this for 2 weeks continuing to water the root ball. I moved it 2 days ago with no problem whatsoever. The root ball was contained and I did not even lose a bloom. I received this advice from Pete41. He said that this is the way the professionals move older plants. Good luck!