Camera-based 3D object detection in Bird's Eye View (BEV) is one of the most important perception tasks in autonomous driving. Earlier methods rely on dense BEV features, which are costly to construct. More recent works explore sparse query-based detection. However, they still require a large number of queries and can become expensive to run when more video frames are used. In this paper, we propose DySS, a novel method that employs state-space learning and dynamic queries. More specifically, DySS leverages a state-space model (SSM) to sequentially process the sampled features over time steps. In order to encourage the model to better capture the underlying motion and correspondence information, we introduce auxiliary tasks of future prediction and masked reconstruction to better train the SSM. The state of the SSM then provides an informative yet efficient summarization of the scene. Based on the state-space learned features, we dynamically update the queries via merge, remove, and split operations, which help maintain a useful, lean set of detection queries throughout the network. Our proposed DySS achieves both superior detection performance and efficient inference. Specifically, on the nuScenes test split, DySS achieves 65.31 NDS and 57.4 mAP, outperforming the latest state of the art. On the val split, DySS achieves 56.2 NDS and 46.2 mAP, as well as a real-time inference speed of 33 FPS.