Is it okay to put rigid sheet foam insulation directly over studs before installing sheetrock (fiberglass insulation would be in the walls)?
We live in the same area, you will want something that will allow moisture out But stop air flow (vapor barrier). 

We do have issues with mold here.
  on several houses I have found the bad stuff (Stachybotrys chartarum) and 2 have been when the home owner tried to seal the walls In similar era homes. 
 In this era home there are normally a lot of air leaks and house wrap may be a better option, although toxic mold is not common all mold can cause issues with the structure and health at some level.

Also don’t forget about your floor. Your floor is a large external surface area and simple fiberglass insulation in both the walls and floor may be best. I have used chicken wire or fish net to hold the fiberglass in the floors in place and it reduces the chance of squirrels, raccoons and opossums getting in there and pulling it down (yes even in town).  if copper pipe do not let the chicken wire touch the pipe, the moisture in the air + copper+ zinc coated wire = pinholes in copper pipe because of galvanic corrosion. 

If you want to air seal the room please get a dehumidifier. 
Dehumidifiers in a sealed bedroom will go a long way to prevent mold and mildew here in the Pacific Northwest.