Representation learning for knowledge graphs (KGs) has focused on the problem of answering simple link prediction queries. In this work we address the more ambitious challenge of predicting the answers of conjunctive queries with multiple missing entities. We propose Bidirectional Query Embedding (BiQE), a method that embeds conjunctive queries with models based on bi-directional attention mechanisms. Contrary to prior work, bidirectional self-attention can capture interactions among all the elements of a query graph. We introduce two new challenging datasets for studying conjunctive query inference and conduct experiments on several benchmark datasets that demonstrate BiQE significantly outperforms state of the art baselines.