Bumi is actually one of the funniest characters on the show. He happened to be the eldest child of Avatar Aang and his wife Katara. But by the time of The Legend of Korra, he’s a middle-aged man without the ability to air bend or water bend.
He’s definitely got more of Aang’s personality than Tenzin, despite not getting his wind powers. He definitely knows how to tick off his brother, LOL.
He surprisingly gets air bending powers when some unknown force grants air bending powers to people all over the world. Would have sucked for him to be excluded from that, to be honest.
So while he probably didn’t look forward to his little brother training him in airbending, he was too excited to use his powers to care that much.
While he never was a great factor in advancing the story, he was just a big fun goofball. Much like his namesake, King Bumi from Avatar The Last Airbender.