The first thing I'd do is take the cover off the bedroom thermostat and make sure it doesn't have a remote thermistor.
If one doesn't already exist, it may be a bit of a challenge to add one, depending on access from one place to the other. You may be better off moving the entire (or adding a new) thermostat in the bedroom and running the wiring from the A/C to the new t-stat location.
Salem 29RKSS Pushing a GMC Sierra 2500HD!
Gotta go campin!