The word Princess implies that Bubblegum is the daughter of royalty, yet she seems to handle all the duties that a king または クイーン would normally perform. Then the 質問 is: who are the king and クイーン of the キャンディー kingdom, and where are they?
Now, remember that it has been 発言しました that the world of Adventure Time is a post-apocalyptic wasteland that has rebuilt itself into the strange land of Ooo. Bubblegum is one of the few characters who appears to be human. Therefor, if her parents are human too, they could have been destroyed in the apocalypse and she keeps her タイトル as princess in order to honor them.
It is also possible that they have gone missing, and Bubblegum doesn't want anyone to know that anything is wrong. She works so hard and has become so talented at science in preparation to rescue them as soon as she gets word of their whereabouts.