Autonomous driving involves complex decision-making in highly interactive environments, requiring thoughtful negotiation with other traffic participants. While reinforcement learning provides a way to learn such interaction behavior, efficient learning critically depends on scalable state representations. Contrary to imitation learning methods, high-dimensional state representations still constitute a major bottleneck for deep reinforcement learning methods in autonomous driving. In this paper, we study the challenges of constructing bird's-eye-view representations for autonomous driving and propose a recurrent learning architecture for long-horizon driving. Our PPO-based approach, called RecurrDriveNet, is demonstrated on a simulated autonomous driving task in CARLA, where it outperforms traditional frame-stacking methods while only requiring one million experiences for efficient training. RecurrDriveNet causes less than one infraction per driven kilometer by interacting safely with other road users.