With the rapid growth of bike sharing and the increasing diversity of cycling applications, accurate bicycle localization has become essential. traditional GNSS-based methods suffer from multipath effects, while existing inertial navigation approaches rely on precise modeling and show limited robustness. Tight Learned Inertial Odometry (TLIO) achieves low position drift by combining raw IMU data with predicted displacements by neural networks, but its high computational cost restricts deployment on mobile devices. To overcome this, we extend TLIO to bicycle localization and introduce an improved Mixture-of Experts (MoE) model that reduces both training and inference costs. Experiments show that, compared to the state-of-the-art LLIO framework, our method achieves comparable accuracy while reducing parameters by 64.7% and computational cost by 81.8%.