The only way that I'm aware of this working is through using fscommand. There are specific rules, and limitations, but it can be done. The biggest problem is that you can't pass variables to the AppleScript, nor get values in return, or even really know when the AppleScript has completed. And another of the rules/limitations is that this has to be done from a projector, it can't be done from a SWF running in the browser or the standalone player. I am not sure if an AIR app will let you run the AppleScript through fscommand. But if it could, then there's potentially a way around the argument/return issue. I would theorize that you could write your arguments out to a temporary text file, then run the AppleScript, which could read that text file and parse out the arguments, run its thing, and perhaps write out return data back into the text file. The thing is knowing when the AppleScript has finished; I suppose you could poll the text file every few seconds until you see a change...
Well, all of that is speculation anyway, as my hunch would be that you couldn't run fscommand AppleScripts from AIR in the first place. But it's worth looking into. The docs do mention the "exec" only works from a projector.
So, I had been sitting on a blog post that describes how to do this fscommand thing for a while, and this question prompted me to finish it up, and post it, so that I could just link to it to give you the details you need, if that's the solution that would work for you:
http://summitprojectsflashblog.wordpress.com/?p=738