Yes. she is definetley showing some alpha behavior. In the four days you have had her you must have unknowingly shown her some cues that she is alpha over you. What are your feeding habits like w/ her? I have often heard you are supposed to make the dog "sit/stay" before taking their food and also let them see you fake eat from their food bowl (b/c the pack leader always eats first). Also collar/leash lead walking is good way to teach pack order. I would start crating her at night b/c she thnks the bed is her's, if she become agressive in bed immediatley place her on the floor. You said she was how old? You can retrain it will jst take persistence and patience.
