Has anyone ever used the Sierra Vista Airport to stash a car? Seem pretty simple to ride to start from there.

https://www.sierravistaaz.gov/city-departments/public-works/airport/

"Parking
Long and short-term parking is available at the Sierra Vista Municipal Airport, at no charge."

This would be a good option.  The SV Airport is a relatively safe place to leave your car. 

OK - trying to figure this out... East Coast person here, we hang our food in the trees so that bears and critters don't eat our food at night.  I have just a tarp for a tent and trying to figure out what you do on the AZT in the desert where there are no trees to hang food?

If you're in a part of the desert that doesn't have trees, then most likely you won't have to worry about bears.