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The efficacy of zero-shot sketch-based image retrieval (ZS-SBIR) models is governed by two challenges. The immense distributions-gap between the sketches and the images requires a proper domain alignment. Moreover, the fine-grained nature of the task and the high intra-class variance of many categories necessitates a class-wise discriminative mapping among the sketch, image, and the semantic spaces. Under this premise, we propose BDA-SketRet, a novel ZS-SBIR framework performing a bi-level domain adaptation for aligning the spatial and semantic features of the visual data pairs progressively. In order to highlight the shared features and reduce the effects of any sketch or image-specific artifacts, we propose a novel symmetric loss function based on the notion of information bottleneck for aligning the semantic features while a cross-entropy-based adversarial loss is introduced to align the spatial feature maps. Finally, our CNN-based model confirms the discriminativeness of the shared latent space through a novel topology-preserving semantic projection network. Experimental results on the extended Sketchy, TU-Berlin, and QuickDraw datasets exhibit sharp improvements over the literature.