There are several problems I read here. Although it wouldn't hurt to insulate the ceiling under the room, I don't think that is your problem. You mention you did not see a return. It may have one but doesn't sound like it to me since you mention you keep the door to the room closed and the temp. drops drastically. If you are not taking air out of the room, you won't be letting conditioned air in. The size of the room also causes me to suspect there should be 2 supplies and 2 returns (without knowing the size of your existing system). You mention this room is an addition. I suspect the supply, return, heating, cooling systems were designed for the original sq. footage and was not upgraded with the addition. That doesn't mean things can't be done to improve what you have now. For us to really give you much in the way of more precise helpful information, we're really going to need much more information in return. We can steer you in a direction but you will need to have a qualified tech. to come in and do load calculations and make a true assessment of what really needs to be done. Just sitting here reading what you have mentioned, I can only guess (from experience) that you need some rework done. I may be wrong...maybe the original design was to allow for this addition. A Tech doing a site survey can surely better determine that.

Just to be clear, the bedroom has two registers and a cold air return. The storage room/crawl below has one register and I confirmed there is no cold air return in that space.

Ok, I misread your post and interpreted the room above the space only had 1 duct, sorry! I'm not too sure the one duct into the storage area will do much without a return duct but would not suggest one be added due to what is stored in there. This leads me to think there will be a chance for some humidity. I personally would be cautious about storing anything with gasoline under the bedroom, withoutsome sort of fire proofing. There are codes governing it so you may want to look into that.
To be on the safe side to address dampness and a very low level of fire and fume protection, I would suggest r-13 insulation with the foil backing toward the space. Use the wire insulation supports and the job will go very quickly, neatly and securely. I doubt you'll be getting condensation in the storage area but keep an eye on it. As small as the ceiling area may be, how about finishing the ceiling with some sort of fire proofing or at least cement backerboard? I don't know if you are puting a gas mower in there or not but that would help delay fumes and the smell of decaying grass clippings from getting into the bedroom above.

I would definitely insulate the floor new space aka the cieling of the new crawl space, and the vapor barrier should be against the warm surface, directly abutting the floor. It might be useful to put a thermometer/humidity meter in that crawl space to find out how much variation it undergoes. If the walls of the new crawl space are not insulated, you might want to do that too, especially since the space is not ventilated. You might also consider putting in a plastic vapor barrier on the floor of the new crawl space, if it does not have one.

Thank you for your replys.

Looks like I will try the ceiling insulation and perhaps put some foam on the small uninsulated area of the foundation. Since I only store lawn equipment in this area with the tanks dry, fire & fumes should not be an issue.