While there is no real-world meaning for the name, Rowling has said that she chose it because it sounded "wise and ancient" and fit the character's personality.
It is possible that she drew inspiration from the word "bumblebee," which could relate to Dumbledore's love of music and his somewhat clumsy demeanor. The "dor" suffix might also be a reference to the word "door," symbolizing his role as a guardian and guide.
However, ultimately, the meaning of the name is left open to interpretation, just like many other aspects of the Harry Potter universe.