The Bridgerton series, including the character Charlotte Bridgerton, is not a true story in a literal sense. It's a work of fiction created by Julia Quinn. But it does a great job of depicting the social norms, fashion, and courtship rituals of the Regency era. For example, the grand balls and the importance of family reputation in the story are all things that were very much part of that historical period, but the specific characters and their individual stories are made up for entertainment purposes.
Yes, the character Charlotte Bridgerton is part of the 'Bridgerton' series which is based on a set of novels. However, while the stories are fictional, they are set in a historical context that draws inspiration from the Regency era in England. So, it's not a true story in the sense of being a historical account but has elements that are reflective of the time period.