Is the bedroom AC located in a confined space and air rapidly cools and kicks off the thermostat? Somehow recirculating cold air into the thermostat space? If so a remote thermostat could help. If not I'd suspect the thermostat being defective or the probe located improperly. The fact it only runs four times per hour could indicate that. Best to post the make/model and some of the forum experts on AC could chime in.
I had similar situation in my house where thermostat was much to close to forced air register. The air conditioning would cycle off much too soon-and the solution was relocating the thermostat.
