Anyone who has lived with cats knows that changing the behaviour of a feline is next to impossible, unless the cat thinks the change was her idea. This extends to the cat that bullies other cats in the home. The best way to deal with the bully cat is to change the environment, giving the other cats better opportunities to escape the bully, and access the litter box, food, water and affection. As the stress levels in the home decline because the other cats are able to escape the bully cat's attention, the bullying behaviour should decline.
Spay/neuter the bully cat, and any other cats in the home, if the felines aren't already altered. Unaltered cats, with hormones running rampant, are much more prone to bad behaviour, including bullying and other types of aggression.
Add litter boxes. The litter box is a big deal in the cats' world and much fighting and bullying in multi-cat households centre on access to the litter box. The general rule is that you should have one more litter box than you do cats. This means, for example, that if you have four cats, you should have fiver litter boxes.
Place the litter boxes in different locations throughout the house. If the bully cat is guarding one box and not allowing the other cats access to it, the other cats can go to one of the other litter boxes in a different location. The bully cat can't be everywhere.
Provide escapes at different levels. Cats like height. If the cats can get away from each other--and especially the bully cat--stress will be reduced. Providing these escapes can be done in several ways. Adding cat trees is the most expensive options. Simply cleaning off bookshelves at different heights, or making the top of the refrigerator available as an escape, works equally well.
Establish several feeding areas, if you have food out for your cats at all times. This will allow other cats to access food and water when the bully cat is guarding a particular area. If you have set feeding times for your cats, feed the bully cat in a separate room where he can't antagonise the other cats while they are eating.
Set out water bowls in several areas. This will allow the other cats to drink if the bully cat is guarding a particular water bowl.
Feliway, a product that mimics the "happy" pheromones your cat releases when she rubs against your leg or a piece of furniture, can help to ease tension in a multi-cat household and may help to stop the bullying behaviour. Feliway is available both as a spray or a diffuser. It is available at pet stores or from your veterinarian.
Behavioural problems, including bullying, can sometimes be caused by a medical condition. If your cat's behaviour doesn't change after you have made adjustments to the environment, you should take the cat to a veterinarian for a complete medical checkup. Any kind of pain, as well as various disorders, can cause aggression in a cat.