Q.do burning bushes self propagate?
There are small plants around my burning bushes. Are these new burning bushes?
Burning bush is a self-seeder and in fact, you can propagate it from the seeds - this article will tell you how:
https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-propagation.htm
However, what you are seeing around your burning bushes are root suckers, which is another way that the burning bush propagates itself.
For more information on growing burning bushes, please visit the following link:
https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm