Window Air Conditioner Needs Repair
If your bedroom has a window air conditioner, it may be leaking condensation from its pan back in to the room. This can happen if your air conditioner needs to be serviced, or if it is severely under- or over-powered relative to your room size. Look inside your air conditioner from the outside through its ventilation grills and see if there is standing water in the case. Also check the area surrounding the air conditioner on the inside, and see if you feel dampness or moisture. Have your air conditioner serviced or replaced by a licensed repair person.
Central Air Conditioner Needs Service
If you have a central air conditioning unit, it may need service if you are smelling a musty smell in your bedroom. This may be due to mold or mildew accumulation in the unit itself, or in the ductwork. Have a licensed professional look at your ducts and unit and determine if it needs service or repair. Discuss your concerns regarding the smell and the professional may be able to help eliminate any air conditioning-related sources.
Run a Dehumidifier
If your smell continues, you may want to invest in a standalone dehumidifier. Dehumidifiers wick moisture out of the air and deposit it in to a basin or container that can be easily dumped or used to water your garden. The musty smell you are smelling may be due to humid air being stagnant, and moisture becoming trapped in your bedding, or the bed itself. Get a dehumidifier rated for a room the size of your bedroom and see if it eliminates your odor problem.
Your bedroom is likely the least occupied room of the house. You spend eight hours in the room each night, and the rest of the time it is closed off from the rest of the house. If this is the case, consider opening the door and placing a box fan at the doorway to help circulate air in to your room and move your bedroom's air out in to the main part of the house. This is especially helpful if you are running a central air conditioner that has an intake located outside of your bedroom. Moving the humid air out of the bedroom will help move it toward the intake, where it will be dehumidified and recirculated.