Policymakers have strongly supported the widespread adoption of solar and wind energy as the two major pillars of the clean energy transition. Yet these energy sources are prone to weather and climate variability, which is often oversimplified in energy system models, resulting in an overly optimistic portrayal of these technologies as silver bullet solutions. Bioenergy, with its inherent flexibility, can mitigate the negative impacts of the intermittency of renewables on a net-zero emissions energy system. As it takes two to tango, we analyze the interplay between Variable Renewable Energy (VRE) and dispatchable bioenergy, considering the past weather data using a risk-sensitive stochastic optimization model and future climate scenarios for Germany. Our outcomes suggest that when solar and wind energy are abundant, the overall system cost is at a minimum, whereas during shortages, flexible bioenergy can support meeting electricity demand, albeit at approximately 5% higher total system cost. Moreover, our findings suggest that excessive risk sensitivity may drive greater dependence on dispatchable fossil energy, which poses a serious threat to achieving climate targets. While Germany serves as the case study, the methodology developed is universal and can be applied to other energy system optimization models with different geographical scopes, painting a more realistic picture of the future predicaments and solutions.