I had the similar case like yours a year ago. Therefore, probably I can share my experience with you. I inherited a lot of antique roses with the purchase of an apartment and in the heavy bush there a lot of rose bushes hidden.
I live in Europe, and usually we are allowed to replant or re-allocate during autmn and early spring, when there is no threat of snow, frozen ground, and strong sun.
If you are able to wait until atumn it will be ideal to do the relocating of your rose bush, when they are half alseep. You can prune back the bush and dig the rose out, with as much root system as possible. Dig a hole at least 4 times larger then the rose and make it is deep enough. Do not provide any fertilzer.
If you cannot wait till autumn to relocate your rose, you can also prune back the bush and dig the rose out. However, there is a certain high risk that you might loose the rose. Make sure you choose a time when there is no threat of hot direct sun when you place your rose bush into the new location. Try to keep and retain as much as possible the root system. Try not to pull , when you dig your rose out. After you have digged out the bush, place it immediately into a container where there is some mixture of loamy soil and water. The mixture should be loamy that sticks onto the roots and help the roots regain their moisture. Let the root stand into this mixture with water for an hour to 3 before planting into the ready digged new location. Do not add any fertilizer before you see new growth after 3 months. Lastly, make sure you water the rose bush regularly.
Hope it helps.