We examine the problem of a generator offering generation and ancillary services from a set of cascaded hydroelectric units to a centrally dispatched market that does not account for watershed constraints. By modeling the least-cost dispatch problem and computing the resulting schedules and market prices, we formulate a stochastic bilevel optimization problem that maximizes the generator's expected profits under different demand and supply realizations. To account for potential infeasibilities in the resulting hydroelectric dispatch, we include penalties in the generator's objective function. We propose a simple technique that replaces the lower-level dispatch problem with its linearized Karush-Kuhn-Tucker optimality conditions to convert the problem to a single-level mixed-integer program. We use two numerical case studies, based on actual river systems, to demonstrate the benefits of the proposed model.