What I mean by this is: take waterbenders for example--they need water to bend. This is an external source for their bending. An example of an internal source would be firebending, since it comes from their chi. So do airbenders rely on an external source because there is air in the world, or does it come from inside them like firebending?
The way you define the difference between an external and an internal source, air benders usually rely on an external source (I'd call it bending material) - air - but true flight/levitation and some spirit-related abilities like spirit projection (that may or may not be counted as air bending techniques) do not since they rely on the spiritual energy of the bender and do not manipulate air but only the bender themself.
But this relates to what I would call bending material and you asked for the source. Unfortunately, we have very little lore regarding the source of air bending. We know water bending relies on the moon and the ocean and fire bending relies on the sun at least to some degree. avatar.fantom.com names "air" as the source of air bending, and "earth" as the source of earth bending. However, this is not backed by any reference or lore and it is unlikely that it is the (whole) truth since we have no confirmed lore to support this and the wiki only mentions "sun" as the source of fire bending but we know that a powerful comet can also fuel or enhance fire bending. It is unlikely that only water bending is rooted in the spirits - especially since air bending has a way deeper connection to the spirit in the first place.
So all in all, all bending styles have an external source to some degree even when we know close to nothing about the sources of air and earth bending and all bending styles require bending material for most of their techniques with the distinctiveness that fire bending is the only bending style that usually needs nothing but the benders own chi as bending material.