Bundle Adjustment (BA) has been proven to improve the accuracy of the LiDAR mapping. However, the BA method has not been properly employed in a dead-reckoning navigation system. In this paper, we present a frame-to-frame (F2F) BA for LiDAR-inertial navigation, named BA-LINS. Based on the direct F2F point-cloud association, the same-plane points are associated among the LiDAR keyframes. Hence, the plane-point BA measurement can be constructed using the same-plane points. The LiDAR BA measurements and the inertial measurement unit (IMU)-preintegration measurements are tightly integrated under the framework of factor graph optimization. An effective adaptive covariance estimation algorithm for LiDAR BA measurements is proposed to further improve the accuracy of BA-LINS. We conduct exhaustive real-world experiments on public and private datasets to examine the proposed BA-LINS. The results demonstrate that BA-LINS yields superior accuracy to state-of-the-art methods. Compared to the baseline system FF-LINS, the absolute translation accuracy and state-estimation efficiency of BA-LINS are improved by 29.5% and 28.7%, respectively, on the private dataset. Besides, the ablation experiment results exhibit that the proposed adaptive covariance estimation algorithm can notably improve the accuracy and robustness of BA-LINS.