To be fair I doubt bumi has had to fight a lava bender, its like amon amon had no practice against air benders, air bending kicked his arse, even the equilsists were powerless against tenzins kids, there was no one to practice against. Kya did ok she was up against zaheer and water arm lady both of which are not good match ups for her altough I'm sure she had some spars with tenzin and aang here and there. Plus I found her fight scenes to be awesome.
Amon was caught off guard because Korra suddenly started airbending while he just locked her bending powers and while she never could airbend before. On top of that they were in a relatively small contained space. If Amon had known it before, I doubt it would have gone that smoothly and Amon is something else than the regular Equalists as the latter lost regularly to any type of bender and they were able to catch all of Tenzin's family. Not to mention the fighting style of the Equalists resembled the movements of airbending quite a lot.
Bumi on the other hand knew about the lava bender and he is supposed to be a very experienced soldier who, according to himself, should have been stuck quite a lot in dangerous situations. That he was fighting a lava bender for the first time I find no excuse as he seemed to completely improvise everything with desperate attempts to attack like biting. Even though it was funny to see, I was expecting of him to show more as why he was such a high-ranking soldier, especially when he lived a large part of his life with benders. Inadvertently he even showed the lava benders weakness: he can't lava bend in very close proximity of him or it would backfire. To kick Bumi off he had to earthbend, but Bumi showed no signs of this all being a deliberate discovery nor that he even realized it. I didn't expect him to win, but in the least show some Bumi-ingenuity just like Sokka, that other non-bender, did.
And as a bending daughter of Aang & Katara I expected more of Kya. Tenzin is the youngest, but he was evenly matched with Zaheer, while Kya got served first by Zaheer and then even by the water bending lady.