Answer: Unfortunately, it can be difficult to move a rose that has been growing well in one place for such a long time, they usually have extensive root systems and the move can be a big shock to the plant.
Roses will not grow healthily in a heavy clay soil that does not drain well, so if the new soil is truly a clay then they would not grow well in it without some extensive attention to improving the drainage such as a raised bed or underground drainage system.
All in all, you might want to leave it where it is. If however you decide to move it, the best time would be when it is dormant during the very early spring/late winter or in late fall. (If it is leafing out then it is a bit late to try this spring.) Be sure to take as much of the rootball as you can and water it carefully the first season just as you could a brand new plant.
You would also want to amend the soil as indicated by soil tests, your county extension should be able to help you with the tests and interpreting the results with an eye on growing a rose bush in that location.
Another option might be to purchase a second one and plant it at the new house. This is a popular rose that has stood the test of time and should not be too difficult to locate.
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