Here's a list of what type of bender the Gravity Rises characters would be if they had bending abilities from Avatar: The Last Airbender. 

Note: I have a crossover between GR and ATLA that can be seen in my List of Gravity Rises AUs chapter. This, however, is what type of benders the canon GR characters would be. Most of these will be different from the bending in the GR/ATLA crossover.

Mabel: Firebender (she's scared of her powers, particularly of hurting people with them)

Dipper: Airbender

Gideon: Airbender 

Pacifica: Waterbender (she knows how to bloodbend... she scary)

Ford: Firebender (he teaches Mabel to use her powers and helps her not be scared of them <3)

Lee: Earthbender

Melody: Earthbender (earthbenders are described as loyal and immovable, and that definitely describes Melody)

Robbie: Earthbender

Wendy: Firebender (she uses her fire to burn artistic designs into things)

Fidds: Waterbender

Candy: Earthbender (she'll fight you with it)

Greyson: Earthbender (he won't fight you with it)

Gideon and Pacifica both use their bending to have similar effects to the amulets. For example, Gideon uses his airbending to fly, and he can use spiritual powers to wipe memories for the Order. Pacifica can use her bloodbending to physically control people (whether or not she can only do it on the full moon, like in ATLA, or all the time, like in LoK, I'm not sure). Dipper is a master of the airball and can be found zooming around the house at any given time. And, like it says above, Ford helps Mabel learn how to firebend without destroying things.

What type of bender are you? I'm an airbender :)