Spring and fall are fine for planting hydrangea bushes; most sources I found recommend waiting for cooler weather and transplanting the bushes in late fall or very early spring while the plants are dormant but the soil is workable.

What is the best time to move hydrangeas?

In cooler climates, the best time for moving hydrangea bushes is November, when the bush is dormant but the ground is not yet frozen solid. In warmer climates where the ground doesn't freeze, you can do your hydrangea transplanting between December and February.

Can you dig up and move hydrangeas?

Transplanting Hydrangea Tips

When digging a hydrangea to transplant, dig up as much of the rootball as possible. Since the roots are fibrous and form a ball filled with soil, the plant may be VERY heavy, so you might want to get some help with this. Replant the hydrangea in an area that is shaded during the afternoon.