Hydropower producers participate in the electricity market by providing bids in the day-ahead market auctions. Making good bids that obey all market rules and consider uncertain prices for large, interconnected hydropower watercourses is challenging. This investigation aims to find bidding strategies that attend to the market aspects and all constraints relevant to short-term hydropower production. This paper presents a stochastic mixed-integer nonlinear model and a nonlinear heuristic method for the bidding optimization problem and shows a comparison of the model's performance in two case studies. The comparison of the two models shows that their results are close and that the heuristic method can reach the optimal solution after a few iterations. The numerical experiments are also compared with results from the Short-term Hydro Optimization Program (SHOP), which is a software used for operational planning in the Nordic electricity market.