The best time to transplant a burning bush is usually during the rainy season. When a burning bush is transplanted during the rainy season, it is able to grow into a mature tree.
As there are three or four different plants called burning bush and all require different treatment it is impossible to answer this question accurately.
Just before the fire goes out.
Hawthorn bushes transplant best in spring. They grow very well just about anywhere as long as their roots find well-draining soil.
Mount Sinai
Summer
In the fall tends to be the best time to transplant firebush [Hamelia patens], and indeed just about any plant. Specifically, a popular autumnal month tends to be October. The reason lies in getting the plant adjusted to the new location before the cold weather sets in. By the time the cold weather is over, the plant feels at home in the new location and is ready to bloom on old wood or put out new growth.
Soon after puberty.
The best time is after the first frost and before the last frost of your region. This is because you want to transplant when the plant is dormant.
The best time to plant most trees is during dormancy, so late Fall to early Spring is the best time to plant or transplant hybrid poplars. I feel, if you transplant around December, your trees have plenty of time to get used to their new location before new root, leaf and stem growth begin.
The best time to transplant a peach tree is January. The trees are still dormant from the winter, which will reduce the shock of transplantation. It is also best to transplant a peach tree when it is at least one year old and preferably not after they reach three years old.
Rainy season is the best time to transplant seed. During rainy season, there is a lot of humidity, hence the seed sprouts will get required good quality of water for a better growth.
Spring
Evergreens are best moved in the spring.