Based on the show, people pass on bending to their children, but so far, only can pass on one element. But, we haven't seen enough one way or another to say if elements can be dormant or even dominant over each other.
Based on Katara, Aang, and their children, if bending is passed on like classical genetics (B for bending b for non-benders), anyone who had a B would be a bender. We don't know about Aang's parents, but we know Katara came from a bender and non bender (so at best, Katara would be B/b). If nonbending is the recessive trait, then Bumi would be b/b (meaning that Aang had one non-bender parent), Kya would be B/b, and Tenzen would be B/b. The question becomes though, what happens when B can be Bwater, Bfire, Bair, or Bearth. Then, potentially, Kya or Tenzen could be Bw/Ba. We don't know if Kya has any children, but if Tenzen were Bw/Ba, probabilistically we would think at least one of his kids would be a water bender, but probabilities aren't definitive and I'm looking at him having four kids and technically one of them has never bent, so take that for what it's worth.
TLDR: possible for one of Tenzen or Kya's children to have the other element, but we haven't seen it yet, so no reason to think one element is dominant over the other.
Now perhaps it's the other way, where bending is the recessive trait, and non-bending is dominant. Then both Aang and Katara would have to be b/b. The problem with that idea is that Aang and Katara's children don't work with this idea. How could Bumi be a nonbender? Well, maybe it's because you have to have both traits from the same lineage -- but then Kya and Tenzen couldn't possess their bending abilities.
TLDR: if bending is like classical genetics, bending must be the dominant trait over non-bending.
Now, the interesting thing to consider is that Tenzen (Ba/?) is married to Pema, a nonbender (b/b). His three children must be Ba/b which is only a .125 probability (.0625 that their baby is also a bender, which Katara suggested). So another possible explanation is that air is dominant over water, but a bender can only pass on the element they know -- So Tenzen is Ba/Bw, but the Bw is overwritten by his Ba.
So, in conclusion, we have no idea what happens when a person receives multiple elements from their parents, because we just haven't seen it. And bending might not follow classical genetics, meaning that I just was wasting time instead of figuring out eigenvectors..
Wasn't that fun~
(I couldn't remember if you have to use the / or not.. it's been a few years since I studied genetics..)