Autonomous assembly has been a desired functionality of many intelligent robot systems. We study a new challenging assembly task, designing and constructing a bridge without a blueprint. In this task, the robot needs to first design a feasible bridge architecture for arbitrarily wide cliffs and then manipulate the blocks reliably to construct a stable bridge according to the proposed design. In this paper, we propose a bi-level approach to tackle this task. At the high level, the system learns a bridge blueprint policy in a physical simulator using deep reinforcement learning and curriculum learning. A policy is represented as an attention-based neural network with object-centric input, which enables generalization to different numbers of blocks and cliff widths. For low-level control, we implement a motion-planning-based policy for real-robot motion control, which can be directly combined with a trained blueprint policy for real-world bridge construction without tuning. In our field study, our bi-level robot system demonstrates the capability of manipulating blocks to construct a diverse set of bridges with different architectures.