Is there another bed for her, and if so, is it similar to the GSD's bed?
Canyx is right, letting them "figure it out" doesn't work for all dogs. I have one now that was raised in a "let them figure it out" household and though she didn't resource guard in her last household (she always had other dogs resource guarding things from her), she started resource guarding immediately in my household. My other dog never resource guards and actually tries to give the resource guarding dog toys. Though she does always want what the resource guarding dog has. They both want what the other has. Based on advice from here and my trainer, I started out keeping them separated by baby gates most of the time and only allowing them together when I was there to supervise. It has mostly paid off as the resource guarder no longer guards food or me but she still tries to guard toys so we don't leave toys around the house. They only get toys when I can supervise or when they are alone or in their individual crates. Its important to learn to read your dog to see before it escalates, my dog starts out by going stiff, then she growls and bares her teeth, then she snaps. The moment I see her go stiff, I call them both and grab some treats and start a training session to bring the tension back down.The whole 'let them figure it out' thing can work for some dogs. But it can also cause one or both dogs to escalate over time.