Bending is a combination of spirituality, culture and genetics. I like to think that during his tenure as Avatar, Aang will spread the philosophy and teachings of the Air Nomads to others. There's bound to be some people still alive that have a great-great-grandparent that was an Air Nomad; we know that even though the Air Nomads were more spiritual and possibly more reclusive than the other nations, the majority of their race was spread throughout the world, not just in the Air Temples. I find it inconceivable that at least some interracial breeding didn't go on, which makes it very possible for Airbending to make a comeback, and for the Avatar cycle to continue. After all, there will be 3 whole generations in between Aang and the next Airbending Avatar, which is, I think, enough time. Of course, there will (presumably) be Aang's direct descendants, as well.
Unfortunately for Appa, since the ancestral habitats and herds of his species were culled over 100 years before the start of the series, I doubt that the Sky Bison have managed to survive. Even if there were some scattered survivors, the severe reduction in numbers would cause serious inbreeding depression.
Oh, and by the way guys, it's "Katara", not "Kitara".