I think most dogs dislike people leaving without them. I know Cadbury whinges when I leave without him (he is a lab). He really can't see why he isn't going too!
Its more pronounced with me than the rest of the family because he is my dog so we have a strong bond. Apparently yesterday when I left the house he whined for a while.
I have also noticed when he was younger and I was gone for a long period (all day for instance) even if he had someone with him when I came back he would be very mouthy and wanted my absolute attention. If I dared talk to someone else he would chew on my arm or tug on my clothes. He definitely got told off for that and I would leave the room without him so he defeated the purpose.
Anyway, what I would suggest is a stairgate positioned either in the doorway to a room or in the hall. That way she can't get to you to bite. I would stand outside the stairgate when someone leaves and if she starts barking rattle a bottle, or use a squirt bottle or a firm no, depending on what works. Once she quietens then praise and reward her.
I don't know how long this will take to work. But at least you will be spared the bites and if all else fails, find a good dog behaviourist in your area and ask their advice.
Good luck.