Rate control allocates bits efficiently across frames to meet a target bitrate while maintaining quality. Conventional two-pass rate control (2pRC) in Versatile Video Coding (VVC) relies on analytical rate-QP models, which often fail to capture nonlinear spatial-temporal variations, causing quality instability and high complexity due to multiple trial encodes. This paper proposes a content-adaptive framework that predicts frame-level bit consumption using lightweight features from the Video Complexity Analyzer (VCA) and quantization parameters within a Random Forest regression. On ultra-high-definition sequences encoded with VVenC, the model achieves strong correlation with ground truth, yielding R2 values of 0.93, 0.88, and 0.77 for I-, P-, and B-frames, respectively. Integrated into a rate-control loop, it achieves comparable coding efficiency to 2pRC while reducing total encoding time by 33.3%. The results show that VCA-driven bit prediction provides a computationally efficient and accurate alternative to conventional rate-QP models.