I'm gonna go out on a limb and say this:
For the sake of having a spiritual-connection with the show (let's be real here, bending isn't possible in the real world), it's nice to think that a bender gets his/her ability by being born with spiritual and mental traits regarding that element.
It doesn't completely fit, mind you. It makes you wonder why Katara's mother wasn't actually a water-bender, because by the implied qualities of her throughout the show, she had the good-hearted, helping and bravery of a water-bender.
Maybe nobody has ever tried. Maybe if you're not born a bender you can meditate and change yourself enough to learn it (or beg the avatar to give you the ability).
The problem with this topic is that only the deep thinkers really get here, and sadly, the show NEVER went into detail about it. It did have those twins and Mako and Bolin, but it's never really explained thoroughly. If you're reading about this, you were probably one of those people who were wondering about non-bender oppression and bloodbending before you even finished the first season of TLA.
I'm just saying that if everyone here wants to have a bit of fantasy in their lives, it would be smart for the writers to one day say that bending is quality of heart and can be attained through mental concentration and determination, so that way we can all feel a little bit less hopeless
*** Edit ***
Apologies, I returned to this and realized my answer didn't pertain to the question too well. It was later in the evening, I was tired and I had a differrent topic in my mind.
So whatWhat determines a bender's element? According to the show. It, it depends on 2two things, one. One is the environment your born toointo. If youryou're born around other waterbendersWaterbenders or in a specific tribe of people, that will determine your element. SecondThe second thing is your mentality, an earthbender. An Earthbender will not be born in the waterWater tribes because the charactoristicscharacteristics of an earthbenderEarthbender do not thrive in those enviromentsenvironments. Same goes tooThe same applies to all of the elements.
So in short, your bending element is determined by the enviroment ofenvironment in which youryou're born, and your mentality (which grows in the shape of your enviromentenvironment anyway).
Its obviously not based on genetics, because kataraKatara had 2 non-bendertwo nonbending parents, but she WAS born in a watertribeWater tribe and had the mentality of a water-benderWaterbender.
UntillUntil the show states otherwise, that would bethis is the safest answer to assume.