My thought was to leave the cat in the bathroom when you're not home, not the dog.
In my experience dogs' attitudes toward cats can be very individual and even depend on environment. For instance, my first Rottie was excellent with my cats, but then she was raised with them. At that time I was still letting my cats go outside, and she was good with them inside and out. However, if a strange cat came into the yard, it was prey, and she could tell a strange cat from her own at great distances. Take her to a friend's barn, and she'd have to be restrained to keep her from going after the barn cats there.
Later I fostered rescue dogs who were okay with cats inside, but would go after the same cat outside. Go after one cat but not the other. So from my experience, I'd never let any dog chase one of my cats. I'd stop it and make sure the dog understood that was a no go behavior. And I'd never leave a cat loose with a dog that showed any tendency to chase when I wasn't there and paying attention.
Some dogs really are mellow with cats, my Akitas were like that. I fostered some rescue Rotties that were like that. But for a dog that chases or even stares at cats - call me excessively cautious but the price the cat pays if I'm not cautious enough is too high. So, cat in safe place before I leave the house. Dog crated at night when I'm asleep.