Bathroom above the Garage

Jonathan, your problem is very common. Do you know what is in the floor for insulation now? Assuming there is some f/G batts or something similar, it would be hard to try to add anything else, such as high density cellulose directly into the cavities. As much as you probably don't want to hear it, the best way is going to remove the sheetrock from the garage ceiling and remove the existing insulation. With the framing completely open, be sure to seal all holes through joists and floor areas where wires or other components may pass thru with foam. The absolute best insulation would be to have a high density foam sprayed into each bay and into any voids along garage door headers etc. This would give you the maximum R value and absolutely stop any cold air infiltration to the bedroom above. The goal would be to achieve an R value of 30 or more. The alternate method for DIY would be to again, seal any air passage ways and door headers with spray foam, then carefully install the max amount of f/g blanket and cover entire field with 4 mil poly and tape all seams and edges with tuck tape before reinstalling your fire rated sheetrock. This is not the best solution as the r value of the f/g is going to be limited by the size of the joists. 2X8 for example will limit you to about an R 23. A slightly higher R value could be achieved with blown in high density cellulose after sheetrock is installed, in place of the blanket f/g insulation. The spray foam is definitely the best overall, but the most expensive as well.

In response to Sharp Tooth's answer, too long for comment section: I have seen 2 to 4 inches of rigid foam insulation added to garage ceilings in this situation. The only drawback of this method is the problems it causes with garage door openers and suspension hardware. It also can cause issues with overhead lighting and overall head space. I hate to be a nay sayer, but I have to negatively comment on your other suggestions. Insulating a garage that does not have new style insulated, airtight doors is a total waste of money. Likewise, trying to heat a garage that is not build to be energy efficient can be extremely expensive to install and fuel, especially if a separate zone or plumbing needs to be added. This is not a viable solution as every time the garage door opens, out goes all that expensive heat. Carpeting, even over a thick foam pad will not help much either, maybe a gain of 2 to 4 "R", quite negligible. I hope you were not serious about heat tape under the ceiling. Other than electric or forced hot water radiant heat grids that would be installed under the floor, not under the ceiling, there is no safe product to do what you decribed. It would not work anyway, since the source of heat would be on the wrong side of the insulation and the vast majority of the heat would be wasted into the garage air. Sorry to shoot down your suggestions, but I truly believe questions should have informed, proven solutions, not wishful guesses.

Rooms above garages are often done improperly. It's amazing, because it really isn't all that difficult, but a lot of people seem to mess it up.

Unfortunately, there's no "easy" way: You're going to have to remove some drywall to inspect and see how the insulation in the ceiling is done. There may or may not be a gap in the space, depending on how the ceiling was done. Even just taking the temperature above the insulation in that space will tell you a lot (above the insulation, it should be close to room temperature).

Drafts in that space are absolutely killer, it means there is a direct source of outside air. Black on the insulation is a good sign of airflow, indicating drafts.

Basically, if the ceiling space isn't totally sealed, the only thing you can do is turn the garage into a conditioned space (very expensive, in terms of both construction costs and ongoing energy costs), and even then, if the problem is between the insulation and sub-floor, it won't help.

What should be there at a minimum is a continuous vapour barrier, with a layer of insulation on top. The vapour barrier should be sealed to the subfloor or the vapour barrier from the walls above. The insulation should go all the way around the edge (in the headers), so the insulation is continuous from the floors up to the subfloor. There should absolutely be no drafts, exposed concrete, or anything directly connected to the outside that is uninsulated.

The best way (in my opinion) to seal this space is to use closed-cell spray foam, and form a continuous seal across the bottom of the entire subfloor. This gives you great insulation, no drafts, and acts as a vapour barrier as well (vapour barrier is not needed in this case -- though some building inspectors still don't understand this, so check your local codes). It also is better at ensuring fumes from vehicles in the garage can't get into your living space (in theory, vapour barrier prevents this as well, but 6mil vapour barrier is easier to puncture than a couple inches of hardened foam).

Though you may be able to find something obvious and fix it, be prepared that there's a possibility that the only "fix" is going to be to completely tear down the ceiling of the garage and re-do it properly.

If you're going to spend money and time on this, do it right.