Yes I would leave the bed made--but with a blanket over the top (and pillow shams) which you do not plan to use and :"fresh" ones in plastic ready to put on the outside layer (things will get dusty in a full month)--or else cover it all with a sheet you can pull off before crawling into bed the first night.
Can your friend open a couple of windows (wide open) for 10 minutes or so whenever she stops by? It will help keep the house from getting too stuffy.
I do not know what base housing is like, but our German apartment starts to smell a bit of sewage as the water in the traps evaporates. If you are gone for more than a couple of weeks it can be icky upon return. You can prevent this by having your friend flush every toilet and run water down every drain (sinks and shower--shower seems to be more important than sink) every couple of weeks. She just needs to run the faucets/shower for about a minute.
Baking soda in the fridge (per pp) or just unplugging it and leaving it propped open is also a good idea.
I am jealous of you living near Ramstein--we read about a Chili's in Germany and did not realize it was on a base at first. The kids and I were so excited to go eat chips and salsa (salsa that does not taste like ketchup!) and then figured out it was not accessible to us--next time you are in there have a margarita for me, will ya?. Oh well, we do get to live down the road from a castle.
Have a great trip to the USA