There are a lot of ways to save water in the bathroom, though some of them might require a bit of an investment at first. Replacing your toilets with newer models like WaterSense, for example, can save 20 to 60% of your water usage. Same goes for your showerheads.
If you’re looking to save money without replacing stuff, it’s all about being conscientious. Don’t leave the sink running while you brush your teeth. Take shorter showers and try not to fill up the bathtub. Don’t throw a bunch of nonsense and trash into your toilet; flush only when necessary.