Answer: The bushes can be moved in fall or very early spring, but it is a huge job because their rootballs will be very heavy. Prepare the new planting area first and make sure the plants are well watered the day before you dig them. Cut them back so you can handle them and to compensate for root loss, then dig them with as large a root ball as you can. Replant immediately at the same depth they grew before. If you haul them in an open truck, cover them with a tarp so they don't dry out and are protected from the wind. Try to select a new location that is well drained, as it would be on a slight slope and prepare the soil by digging in a good amount of organic matter such as compost, rotted leaves, aged stable manure and bedding, or similar materials along with a small amount of sand. You might also consider using a raised bed if your soil is poorly drained or nearly pure clay. Finally, you might run some basic soil tests in case the pH needs adjustment as well. Your county extension (should be able to help you with the tests and interpreting the results.
Once planted, keep the soil slightly moist but not sopping wet and apply several inches of mulch around but not touching the stems and make sure the soil is kept slightly moist next summer and possibly the summer after that until the plants become reestablished. Be sure to follow winter precautions (if any) as done previously, although many of the old shrub roses on their own roots need no special care.
Good luck with the move.
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