I have moved some rose bushes, with mixed success, I think one out of three survived. The problem with the other two is that they were very deeply rooted, so I had to separate them from most of their roots just to get them out of the ground. Plainly it is a good idea to cut it well back so the reduced root ball has less to support.

Except a few species roses, the great majority are grafted onto a rootstock. So if you want to propagate, then grafting rather than taking a cutting is generally the technique you need. Personally I'd just buy a new one. They establish very quickly and many good varieties can be purchased for modest sums.