To ensure a good take on the root system you want a well drained soil with partial to full sun. Dig up the root ball or as much as possible and put it in its new hole and then back fill around the roots. Then tamp the dirt around the plant. This will help stabilize the new plants home.
A moist, sunny area makes a great home for this plant. Dig bush gently and get as much of root system as you can. Place in new area, gently placing roots and plant in hole, cover and water
frequently. Remember roots have to grab hold. Prune back in winter/spring.
First cut the butterfly bush down to about 6" tall, dig around the base of the bush, you can divide the roots if you want, try to keep two to three good roots per each bush, replant in another location.