I took cuttings from my hibiscis trees last fall. They will not winter over here, as it's way too cold. I filled small pots with potting soil. Than I used a pencil & made holes for each cutting & put the cuttings in & pulled the dirt around each one. I then gave them a nice soaking with water. Then the pots were placed in a large ziploc bag & sealed. One pot per bag. I sat them on a windowsill facing north. Evey couple days I would turn the bags, so each side got good light. They have grown nicely & been replanted into larger pots. Once it gets warm wnough I'll repot them into my large outside pots.
You should be able to do this with rose cuttings to. I would dip the cut end in "root tone" first, which is a root growth hormone powder. You can buy it at home/garden centers. I think Lowes carries it or maybe Home Depot.
Any cutting taken from a "hybrid" rose bush may produce a different rose than the adult plant, as several cuttings are used to make the adult plant. They are grafted onto root stock. So you could end up with one of several colors. If it's a really old bush (I have a climber that is over 100 years old) they are on original root & not grafted onto root stock. Those should produce the same plant.