Despite significant advances in neural vocoders using diffusion models and their variants, these methods, unfortunately, inherently suffer from a \textit{performance-inference dilemma}, which stems from the iterative nature in the reverse inference process. This hurdle can severely impede the development of this field. To address this challenge, this paper revisits the neural vocoder task through the lens of audio restoration and propose a novel diffusion vocoder called BridgeVoC. Specifically, by rank analysis, we compare the rank characteristics of Mel-spectrum with other common acoustic degradation factors, and cast the vocoder task as a specialized case of audio restoration, where the range-space spectral (RSS) surrogate of the target spectrum acts as the degraded input. Based on that, we introduce the Schr\"odinger bridge framework for diffusion modeling, which defines the RSS and target spectrum as dual endpoints of the stochastic generation trajectory. Further, to fully utilize the hierarchical prior of subbands in the time-frequency (T-F) domain, we elaborately devise a novel subband-aware convolutional diffusion network as the data predictor, where subbands are divided following an uneven strategy, and convolutional-style attention module is employed with large kernels for efficient T-F contextual modeling. To enable single-step inference, we propose an omnidirectional distillation loss to facilitate effective information transfer from the teacher model to the student model, and the performance is improved by combining target-related and bijective consistency losses. Comprehensive experiments are conducted on various benchmarks and out-of-distribution datasets. Quantitative and qualitative results show that while enjoying fewer parameters, lower computational cost, and competitive inference speed, the proposed BridgeVoC yields state-of-the-art performance over existing advanced GAN-, DDPM- and flow-matching-based baselines with only 4 sampling steps. And consistent superiority is still achieved with single-step inference.