I would not separate them. It is only likely to make them unhappy and lonely. If they are in sight of each other, they may actually become so worked up trying to reach each other that they cause themselves physical harm. I have seen a male bird throw himself repeatedly against the bars of his cage trying to reach his mate. What we have here is a case of bullying, which may pass in time due to a few different factors. If actual violence occurs, they have to be separated immediately. I have a zero tolerance policy for bloodletting, even just a scratch, and I urge others to follow my example in that.
If mating hormones are the cause, making sure their cage is dark with a cover or sheet for 12 hours should break her out of her cycle and end her hormone surge. Budgies breed in summer, and so are stimulated by long hours of light. If she is grouchy from molting, the problem should pass in a matter of weeks. If there are as many feathers as I am imagining, they should be in full molt now. I suggest misting on top of a bath because the more humidity there is in the air, the faster and less painfully the molt will progress.
There is one other possibility, which I doubt is the case here. If your male is sick, the female's natural instinct would be to drive him away until he recovers. It is how a flock avoids epidemic infections. Still, if you have seen no symptoms in him, it does not seem likely. Still, you may wish to watch him a little closer for tail bobbing, feces stuck around his vent, shaggy feathers or any discharge from his eyes, beak, or nares.