A dear friend no longer with us once told me her cat hated water - until she taught him to swim in her backyard pool. Once he got used to water, she could occasionally bathe him inside. While most people think cats hate water, information from Alexander Animal Hospital, cited below, suggests otherwise: "It's simply a myth that [domestic kitties] hate water and can't swim."
In much the same way, I have introduced all our dogs over the years to water (minus a basset hound in the nineties). Alexander Animal Hospital suggests having someone else carry your cat out to your pool or spa to let him see and get a bit used to the water.
"Once your cat has finally been introduced to the water, you will definitely want to make sure they are comfortable and okay with the water itself," Alexander Animal Hospital says. "If so, then you'll want to carry them around in your arms for a bit so they can assimilate to the water for a little bit before diving in.
"Next, as soon as you feel like they are safe and comfortable walking about the swimming pool in the water, then try sitting them down in the water itself while you are still holding them. Fortunately, your cat will most likely begin to paddle before their paws even hit the water. Then, let them go and watch them swim like a natural."
Of course, a bathtub is a good substitute if you do not have a body of water, such as a pool. Follow the suggestions above, and you should eventually have a water-friendly kitty. Then you can move on to a bath. Once your cat doesn't mind being wet, bath time should be easier.
But not all cats require (or appreciate) a scrub-a-dub, according to Purina, cited below. Cats, unlike dogs, usually groom themselves frequently. If your cat doesn't like water, even after following the steps above, a bath might be an unnecessary thing to put him through. Purina says, "That said, even indoors, your cat can encounter dirt or debris, whether from their litter box, food or drink spills, and other messes."
Other reasons your cat might need a bath are his inability to keep himself clean due to a physical condition or fleas, or the presence of paint and other goo in his fur. Purina notes that long-haired cats pick up dirt easier than others, and cats with no fur can't absorb "sebum, the oily substance produced by the body to protect and moisturize the skin." Bathing would be beneficial in those instances.
After several attempts, if your cat doesn't want to have anything to do with water – whether a pool or bathtub - many pet groomers specialize in bathing felines. If you leave it to the professionals, you won't be left with bleeding arms.
Quote to remember: "Thinking is to humans as swimming is to cats." - Daniel Kahneman
Alexander Animal Hospital
"Cat Care: Teaching Your Kitty How to Swim"
"Do Cats Ever Need Baths?"