In many real-world scenarios, an optimal solution for a decision maker depends on the response of another decision maker. This is known as bilevel optimization, which involves two levels of optimization. In this approach, the lower-level problem (the follower) appears as a constraint of the upper level problem (the leader). In practical applications, the follower may have multiple global optima, so the leader must consider the various assumptions about the decision of the follower. This uncertainty caused by the follower’s multimodality poses a significant challenge for the leader in making risk-averse decisions. To address this challenge, we propose an approach for the leader in a bilevel optimization problem. Our approach involves calculating the leader’s uncertainty for a given decision-making problem using a metric that quantifies the level of risk involved. This uncertainty is then used to determine the leader’s optimism and pessimism probabilities. To ensure that the leader is aware of the current risk situation, we impose constraints on their decision-making process. These constraints help the leader make informed choices that minimize the impact of uncertainty. To solve the bilevel optimization problem, we implement a black-box approach that utilizes Bayesian optimization (BO). This approach significantly improves the efficiency of the solution and allows the leader to make more informed decisions in the face of uncertainty. The performance of our approach is evaluated on two test benchmark problems, and we demonstrate a significant improvement in the leader’s uncertainty in these scenarios. Our approach provides a practical solution for decision-makers facing uncertainty caused by the multimodality of the follower problem.