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U-Net, as an encoder-decoder architecture with forward skip connections, has achieved promising results in various medical image analysis tasks. Many recent approaches have also extended U-Net with more complex building blocks, which typically increase the number of network parameters considerably. Such complexity makes the inference stage highly inefficient for clinical applications. Towards an effective yet economic segmentation network design, in this work, we propose backward skip connections that bring decoded features back to the encoder. Our design can be jointly adopted with forward skip connections in any encoder-decoder architecture forming a recurrence structure without introducing extra parameters. With the backward skip connections, we propose a U-Net based network family, namely Bi-directional O-shape networks, which set new benchmarks on multiple public medical imaging segmentation datasets. On the other hand, with the most plain architecture (BiO-Net), network computations inevitably increase along with the pre-set recurrence time. We have thus studied the deficiency bottleneck of such recurrent design and propose a novel two-phase Neural Architecture Search (NAS) algorithm, namely BiX-NAS, to search for the best multi-scale bi-directional skip connections. The ineffective skip connections are then discarded to reduce computational costs and speed up network inference. The finally searched BiX-Net yields the least network complexity and outperforms other state-of-the-art counterparts by large margins. We evaluate our methods on both 2D and 3D segmentation tasks in a total of six datasets. Extensive ablation studies have also been conducted to provide a comprehensive analysis for our proposed methods.