I am interested in this too. Last I heard (which was a very long time ago when AIR was still Apollo) interactive PDFs couldn't be hosted in an AIR app (I think the reason was that AIR only had a very simple PDF render engine).
You can easily render interactive pdf form in air application using htmlLoader :
What I'm looking for is how to communicate between air app. and my LC pdf form that it hosts, it is working with hostContainer method in case I'm using acroform but I don't know if it possible with LC PDF form.
I haven't used the bridge directly (I use it indirectly when it is embedded into a LiveCycle PDF document rendered by Forms ES and called from a Form Guide) but I would assume that it should work exactly the same as calling an AcroForm's hostContainer.