Hi scarebaby. We rent a two bedroom apartment with about 900 square feet. We use our oven often, aren't very good about turning off lights sometimes, have our TV on a lot (we also use it as a monitor for our computer), and keep the temperature pretty comfortable as we are paranoid about developing a mildew problem. We just got our City Light bill yesterday, and it was less than half of yours.
If your fridge, or even your TV, are older that could make a huge difference. My sister is a rents in LA and was recently able to replace an older fridge with a newer, more energy efficient model for free thanks to a grant from the city, and she noticed a significant drop in her electric bill right away. You might see if there is a comparable program for renters here in Seattle.
On a similar note, our management company recently did an energy audit with people from Seattle City Light for each unit in our building to assess where we might be able to save some energy and offered us free CFLs for every light or lamp in our apartment. You might be able to get them to come out and do something similar for your apartment and ask them about the laundry room then. If not, you could always turn off and unplug everything you possibly can in your apartment and take a look at your meter to see what your (almost) baseline consumption is. Then, without turning anything in your apartment on, do a load of laundry and see if that speeds up your meter.