No, you cannot cook on a camping stove using bottled water as fuel. Water is not a suitable fuel source for camping stoves. Camping stoves typically require a combustible fuel, such as butane, propane, or white gas (also known as Coleman fuel), to produce a flame for cooking.
Bottled water is not a fuel; it is simply water stored in a container. Attempting to use water as a fuel source in a camping stove will not generate the necessary heat to cook food.
As for the duration of one liter of water as fuel, again, it cannot be used as fuel in a camping stove. However, if you are referring to using a one-liter bottle of a traditional camping fuel (such as butane, propane, or white gas), the duration of cooking time will depend on the stove's design, the cooking intensity, and the outside temperature. Generally, a one-liter bottle of fuel can last for several hours or more, depending on the stove's BTU (British Thermal Unit) output and the type of food being cooked.
If you are going camping, make sure to bring the appropriate fuel for your camping stove and always follow the manufacturer's instructions for safe and efficient use. Additionally, consider bringing extra fuel if you plan to cook multiple meals or if you'll be camping for an extended period.