I know what "dodging" means, and I know what "bullets" means. But what are dodging bullets??
Literally, it means someone who moved out of the way when someone was shooting at him.
Figuratively, it refers to a narrow escape. "The rumor was that the company was going bankrupt and would close and we would all be out of a job. But at the last minute, we got a big contract to supply parts to an automobile company. We really dodged a bullet that time."