How to store tires in dry California summer
UV rays and ozone are the main factors behind rubber "drying out" -- look at how the Air Force stores its airplanes in the desert: all of the rubber bits are carefully protected from the sunlight. 

So try to keep it in a dry area out of the sun, and not near any ozone sources (mostly electric motors such as an AC unit). 

Note that it's also important that the tire not be subject to any stress or folding that might deform it. For example, if you left the tires on your bicycle over a long period of time, they would self-deflate (due to air migrating out of the rubber) and the very bottom of the tire and tube would deform against the floor - potentially damaging the tire and its casing.

Under the bed is just fine as long as it isn't subject to any pressure or deformation that might come from it lying horizontally while deflated. Hanging the tire (while on a rim) vertically on a hook off the ceiling in a dark place is perhaps the best but might not be practical for you.