Bumi has always confused me. I'm not sure what the writers want to do with him or if he is supposed to be a deep character or purely comic relief. At the end of book 1 were told that Bumi is a wild man, but a good commander and solider, who had Iroh's respect. While Bumi was eccentric in Book 2 they played him as a bit spacey. A lot of his ideas for how to handle situations while comical were so out there that you wonder how he could been a competent commander. However, they showed layers to him than what we saw. He felt out of place in a family full of powerful benders and his inferiority complex to Tenzin and Kya. He even feared that Aang was disappointed in him for not being an air bender. The show was setting up with Bumi's story would involve him getting over his father issues, embrace who he is, and learn he never had to be anyone else. The finale of book 2 gave that resolution to Tenzin and only Tenzin, depriving Kya and Bumi a moment with their father telling them he was proud of them and in Bumi's case that he never had to be a bender.
Come book 3 Bumi is made an air bender. He was probably one of the only ones who had to work at being a decent air bender when others like Kai or Zaheer were naturals. Once again Bumi is played a comic relief that the rest of the family roll their eyes at. Where there are moments for him to shine, like leading or devising a plan to free the air benders from the Earth Queen it instead goes to Asami and he is once again treated as comic relief that doesn't get to do much. Original Airbenders episode shows us more depth to him. He admits he never felt part of the Air Nation before and his resistance to Tenzin's teachings are suggested to be because he still feels out of place. The episode shows us a glimpse of Commander Bumi, by having him rally the air benders together and leading them to free the air bison along with his niece and Kai. In Ultimatum we saw Bumi fight one of the Red Lotus. It was natural for a new air bender to have trouble against someone as powerful as Ghazan, but it got me thinking how did Bumi fight before he was a bender.
Was he skilled with a weapon like Sokka and other non-benders? I personally would have liked to seen Bumi use a staff to give us a glimpse of what he could do with military training. He's out of shape, but it still jarring how Bumi was the only non-bender of Aang and Katara's kids and is treated as purely comic relief (and questionable skills). It's kind of concerning he had to become an air bender to finally be relevant or useful in a fight. I don't get what Bumi is supposed to be, a bad ass normal, military man, the guy who tell tall tales, or the Zuko of the series in terms of embracing who he is and not worry about what he isn't. Does anyone else feel that way or at least feel like Bumi is necessary as a character. Sokka was comic relief too, but he had moments of competence and proved to be an effective leader and came into his own. Bumi feels like what would happen if Sokka stayed the way he was in book 1 of the original series.