Our cat won't drink water unless it's ultrafresh. That means she won't drink it from a bowl, but instead comes running when we're near a sink. She likes to drink from the tap. We can't spend our lives turning taps on for the cat. Your cat is certainly not alone in her fastidiousness where drinking water is concerned.
Cats can be hard to keep hydrated, a situation that can lead to urinary-tract problems.
The more water you can get your cat to drink, the better. That's why I'd recommend doing anything you can to keep your cat happy. Share the bathroom tap with your pet. You can also find continuous-flow feline drinking fountains that recycle the water to make it seem fresh to a cat. You can also usually find them advertised in the back of magazines such as Cat Fancy.