The royal hierarchy (A constitutional Monarchy, to be most specific) within the Earth Kingdom was dissolved by the Phoenix King. Bumi would probably be alive, I see no reason why not, but he wouldn't be a King. Bumi might also have been executed, as he was in fact a royal. 

G3nji, what I will do is issue you a challenge. You create a character and provide me a valid, interesting explanation for what became of Bumi, what he is doing now (if he's still alive) and your lineage, and I will allow you to be the grandson of Bumi. My immediate response upon reading your inquiry was, [i]"Why the [s]fuck[/s] not?"[/i] However, I find the prospect of offering you a challenge to earn what you want as well as allowing a character like Bumi to be rewrote by a player instead of me to be worthwhile. All you have to do is earn it. Impress me.