Securing profits while offering industrial demand-side flexibility in both energy and reserve markets is critical to ensure the profitability of energy-intensive industrial plants to make available their flexible assets in the electricity markets and hence accelerating the energy transition. Proposing efficient bidding strategies for simultaneous participation in the energy and reserve market is challenging since it requires the integration of different market mechanisms in a single optimization problem (combining energy and reserve markets), as well as an accurate mathematical model of industrial processes from which to obtain energy flexibility. Often, such mathematical models are either not available or are described through complex simulators, making the design of a computationally efficient bidding strategy a complicated task. This paper introduces a novel framework to support energy-intensive industrial plants to offer energy flexibility in the joint energy and reserve market. We use a neural network to model the complex nonlinear dynamics of the industrial flexible process. Then, to reduce the complexity of the resulting optimization process we convert the neural network into linear constraints, formulating the problem of bidding energy flexibility into the electricity market as a mixed-integer linear program. The uncertainties of the process variables are considered using a scenario-based approach. A realistic simulation considering the case of an evaporative cooling tower used in the chemical industry, participating in the Belgian electricity market is carried out to demonstrate the applicability of the proposed scheme.