A.P.
I am a vet and would really not recommend spraying the litterbox with a bitter spray. Those sprays do leave behind an odor and a cat has a much stronger sense of smell than any of us. You do not want to use anything that would make using the box unpleasant or you will be in for many worse outcomes. The cat may decide to forgo the litterbox completely and urinate/defecate in other locations around the house. You might be able to try For-bid in the cat's food (I can't remember right now if you can feed it to a cat) to make the stool taste bad for the puppy, but PLEASE do not spray the litter box with anything noxious. Cats need to feel that their litterbox is welcoming. You are right in trying to minimize the dog's access to the box. Having a dog stalking the cat's bathroom could also make the cat turn to other locations.
If putting the box in a corner of a bedroom, bathroom, etc is out of the question you will have to supervise your puppy, training her away from the box. Puppies can be trained but they have to be supervised closely and not allowed the opportunity to eat the stool. I would call your vet for ideas. They or the staff should be able to help you. Good luck!