The water pump scheduling problem is an optimisation model that determines which water pumps will be turned on or off at each time period over a given time horizon for a given water supply system. Water networks, as energy-intensive infrastructures, are promising candidates to offer the power system a reduction in their energy consumption during certain hours of the day; this service is known as demand response. The reduction is typically made during hours when there is a positive difference between the electricity spot price and the contracted energy price. However, both the spot price and the water demand are uncertain. Consequently, the pump scheduling problem with demand response faces several challenges from i) the non-linearities of the equations for the frictional losses along the pipes and pumps, which make the problem a nonlinear mixed-integer model, ii) the uncertainty from energy prices and water demand. These limitations prevent the problem from being solved to optimality in a reasonable computational time in water systems with more than two pumps and reservoirs. Therefore, we developed a new two-step stochastic optimisation model for the demand response in large and high-altitude water supply systems that uses a binary expansion approach to efficiently account for the existing nonlinearities by reducing the computational difficulties while maintaining an excellent representation of the physical phenomena involved. The first step uses a robust water profile optimisation model, and the second step uses a stochastic model for the power profile optimisation with a demand response to obtain the optimum water pump and demand response bidding schedule. We tested this approach using a case study from a mining company's water supply system. Our findings concluded that different seasons and energy policies, such as the minimum power requirement and availability bonus, can significantly impact the water supply system's total costs and the amount of demand response offered to the power system on the capacity market. Additionally, we included a proposal for energy policymakers to create the best strategies for demand response for water supply systems depending on the season of the year and energy prices in order to promote demand response provision on the water supply system operator side.