It took me a while to find this thread, but the notion of Bumi being a "late bloomer" is going to keep coming up, I might as well address the arguments I've been seeing somewhere:
It might be true that Air Nomads always have airbenders when breeding with other Air Nomads, but there's no reason to think that should hold when breeding with an outside population. More specifically, the idea of "a late bloomer whose power was opened with Harmonic Convergence," has a couple of problems on its own:
1. It is generally considered in-universe to be impossible to unlock bending that late in life, or at the very least, it's never been observed before. It generally doesn't make sense to assume an explanation that is very remote if not just impossible, when the simpler explanation is just that he's a nonbender born to bending parents, which does happen.
2. It seems like a distinction without difference. If he wasn't able to airbend without Harmonic Convergence, then effectively he's no different from any other nonbender who got their bending through Harmonic Convergence. It could possibly be that he has a different mechanism for why he's a nonbender than someone like Opal, but with so many things influencing bending, that's probably the case regardless.
Bringing chakras into it adds a few other problems. It's never really said that the chakras actually control the elements they're named after. In fact, the Fire chakra is said to be "blocked by shame," but Zuko's firebending wasn't actually weakened at his most shameful point, but rather his least angry, while he was unable to generate lightning because he wasn't cool-headed enough. These are the only cases we ever see of an emotion affecting bending ability. But supposing that is the case, what could Bumi have possibly experienced to seal off his air chakra at such a young age to prevent bending?
What could be so grief-striking that it prevented airbending when this phenomenon didn't affect anyone else in recorded history? It might be possible, though rather dubious to argue that similar things happened in other populations but people just didn't realize what was going on, but with the airbenders, we know that they always gave birth to airbenders. If someone had their bending unnaturally sealed off due to trauma, they would know.
The final problem is that one could come up with creative answers to all of these points, say maybe that did happen to the Air Nomads but they always knew how to treat it before, or Bumi just happens to be a unique combination of circumstances to allow for an unprecedented event...but at that point, there are so many assumptions to explain why it isn't necessarily wrong that it can hardly be said to be right either.