LV ... it's good news that my guess that the pot would be filled with just roots when you pulled the plant from the pot was wrong.
Aren't roses amazing ? Your rose has gone without food and probably hasn't had sufficient water for a long time, but it went into survival mode and lived. WOW ! That's one of the reasons I love growing roses. Your rose many not have thrived, but it lived !
I agree with Woofie about soaking the rose and you can re-pot the rose in the current container with new soil. After that is done, you still need to prune the rose with the hard prune that I previously recommended. You want to see new growth from the base of the plant, not the top.
You are also at a decision point. Pruning the rose will stimulate the plant to grow new roots and it will have room in the current pot. However, I do think it will outgrow that pot. You have to decide if you are going to replace the soil in the current pot every couple of years, which is what is needed for a container grown rose to thrive, or help the rose return to health and re-pot it into a larger container next December or January which is the time when roses are most dormant in Las Vegas.
Transplanting a healthy rose is much less risky than transplanting a stressed rose.
You now know how to feed your rose in a low humidity, high-heat climate, so if the plant is properly watered, and placed in the right sized container, you should have a thriving rose for years to come ....
btw ... to avoid the problem of the soil being washed away from the root mass that you only found after you pulled the plant from the pot, there is a really easy test you can do for container plants.
When I first plant a rose in a container, before I water it in, I lift one side of the pot to see how heavy the pot is when the soil is dry. Then I water the plant until it won't take up any more water. I wait about an hour and water it again. It always takes up more water. Then I lift the side of the pot again. It is much, much heavier. Now, I know how the pot feels when the soil is fully saturated. Down the road, if I have done a deep watering and the pot feels light, I know I have a problem. I don't have to pull the plant from the pot to know that there is a problem.
That was one of those lessons I had to learn the hard way when I was first learning how to grow roses in containers ....