You recently bought a house that has a bedroom addition above the garage but it is not insulated. Adding insulation should make those rooms more comfortable and save on energy bills. There are several options for insulating above the garage. Depending on the local building codes, the size of the area, whether you decide to hire a professional or do it yourself and maybe the most important factor is your budget.
If you have a sheet rocked garage, the fastest way would be to have blown-in insulation installed behind the sheetrock. A fair warning here, the blown-in insulation may be expensive if your garage is small. If your garage is not sheet rocked you have to install lame-spread rated batt insulation and cover it with sheetrock. First check your local building codes for the requirements of the thickness of the sheetrock for garages including fire safety rules.
The lack of smoke detectors in a garage and the possible storage of flammable and combustible liquids can cause a garage to be considered a hazardous space. This is the reason why you should contact a local contractor to help you in insulating this space.