Bending does not cost any form of mythical energie like aether, mana or however you want to call it. It's in their nature to achieve a level of control over elements - like a good animal trainer can control hits pets, but the pets use their own energy. Of course the question is always: Is his level of control sufficient for this particular task?
Story-wise benders just do things which non-benders might need tools for with their bending ability. Breaking a whole in a wall? Non-Benders might need a jackhammer, earth bender just move the stones out of the way. So bending does not need special actions - it just is a different way of achieving what you could do anyway.
This goes perfectly with Fate, as there is no such system integrated into the core anyway. And we have a nice set of actions which can be used (make sure it's restricted or costly enough though).
More powerful spells you have in mind - which might come in handy more then once - can be defined as stunts.
If you need more, as you have a "see my might and despair" kind of spell in mind that would be too powerfull for "normal" gameplay you still could do it. Similar to the possibility of Fate Core to spend one Fate Point and add a new element into the game: You spend a Fate Point and define the kind of spell you have in mind. The Fate Point is for allowing you to try it though - success is not guaranteed! You will still need to roll the dice on your bending ability - which might backfire. @GM: Obviously the opposition should be notable, but don't make it too hard. He already paid a Fate Point.
Element Bending is an "extra" in the sense of Fate. To make use of this for once you need an aspect describing that your are a bender for a certain element. And you are bound to this element. E.g.:
Last Air Bender
Renegade Nature Bender
Graduate of the Fire Bender Academy of St Canard
And to describe your level of power over said element there are two abilities:
Offensive Bending (de: Angriffsbändigen) This ability is used whenever you attack a target like trying to hurt a person or animal or destroy/break something
Supportive Bending (de: Unterstützungsbändigen) Everything else 😉
This distinctions is made so a character does not become to powerfull because of just one single ability. The narrative distinction between those two is, that Supportive Bending describes your overall understanding of how to use your bending ability to interact with your environment. While Offensive Bending is a more military-style training of how to use your bending in a fight. Similar to how both, Athletics and Fight, comes from your muscles (as well as Physique) - but they use them in other ways, to achieve different goals. And as such the training for both is different.
As said before: Bending comes naturally to Benders, so they switch their attack to their Offensive Bending (if usable) and they switch from Athletics for physical defence to Supportive Bending. Will is still used for defence against mental attacks..
Offensive Bending counts as "short ranged", so it inflicts by default only opponents in the same zone. There are certain stunts to increase the range to 2 Zones, making it behave as Shoot.
If the PC wants to got into hand-to-hand battle or when it comes to overcoming with your bodies strength still Physique is to be used. For handling blades still Fight is to be used, for handling bows/crossbows and other long-ranged weapons still Shoot is used.
Remember: Don't let rules get in the way of story telling!
A few Benders throughout history are known who rely on their Athletics and ability to Shoot with a bow and use their Supportive Bending abilities to improve those selectively. But they don't primarily fight or defend by Offensive/Supportive Bending.