You don't have to get the whole root mass to transplant roses. Get as much as you can and then cut the top growth back to about the same size as the root mass and the rose will be fine. The feeder roots are located closer to the surface of the soil. The deep roots are only anchor roots and really don't feed the plant, so if you leave some behind, it doesn't hurt the rose.
Kathy, I don't know what the weather is like in your area, but if you have high temps, you can still transplant the roses, but it simply takes more work. I think it is better to wait until temps cool down and do the transplant later in the season. If you need more details, let me know.
Whenever you mess with a rose's roots, no matter how careful you may be, you are going to break off a lot of the feeder roots that carry food and moisture to the top of the plant and the food the plant creates through photosynthesis down to the roots. In other words, the roots will be inefficient until it grows new feeder roots.
Dig your planting hole first and perk test it because drainage makes a huge difference in the success of a rose. I back fill only with native soil and don't feed the rose until I see new top growth. That tells me the root system is working. Water your rose daily ... not to the point where it is too wet as that may rot the new roots. The daily watering just compensates for the fact that the root system is not completely efficient until the rose grows new roots.
Good luck with your rose.