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In this work, we address the problem of balancing an autonomous bicycle using direct data-driven control. Firstly, we demonstrate that a direct implementation of data-driven approaches may not guarantee reliable performance, and is highly dependent on how the parameters are selected. To address this issue, we make the reasonable assumption that we have access to some inaccurate information about the system. We use this inaccurate information to design a feedback linearization, based on a simplified point mass model of the bicycle, which does not accurately represent the dynamics of the system. Next, we suggest an inner and outer-loop control strategy. In the inner loop, we implement the aforementioned feedback linearization controller. Subsequently, in the outer loop, we consider the combination of the autonomous bicycle and the feedback controller as a black box, and we design a direct data-driven controller from acquired data. We use a SolidWorks model of a real autonomous bicycle to evaluate the performance of our proposed control approach and to compare it with the direct data-driven controller design derived from acquired data of the bicycle without feedback linearization. The results show that our proposed strategy significantly improves the performance and makes the data-driven control approach more reliable across a broader range of parameter choices compared to a data-driven controller designed based on data from the system without feedback linearization. Finally, we show that introducing an additional integral-like state further enhances the system's performance.