Zero-Shot Neural Architecture Search (NAS) approaches propose novel training-free metrics called zero-shot proxies to substantially reduce the search time compared to the traditional training-based NAS. Despite the success on image classification, the effectiveness of zero-shot proxies is rarely evaluated on complex vision tasks such as semantic segmentation and object detection. Moreover, existing zero-shot proxies are shown to be biased towards certain model characteristics which restricts their broad applicability. In this paper, we empirically study the bias of state-of-the-art (SOTA) zero-shot proxy ZiCo across multiple vision tasks and observe that ZiCo is biased towards thinner and deeper networks, leading to sub-optimal architectures. To solve the problem, we propose a novel bias correction on ZiCo, called ZiCo-BC. Our extensive experiments across various vision tasks (image classification, object detection and semantic segmentation) show that our approach can successfully search for architectures with higher accuracy and significantly lower latency on Samsung Galaxy S10 devices.