Zero-shot cross-domain sequential recommendation (ZCDSR) enables predictions in unseen domains without additional training or fine-tuning, addressing the limitations of traditional models in sparse data environments. Recent advancements in large language models (LLMs) have significantly enhanced ZCDSR by facilitating cross-domain knowledge transfer through rich, pretrained representations. Despite this progress, domain semantic bias—arising from differences in vocabulary and content focus between domains—remains a persistent challenge, leading to misaligned item embeddings and reduced generalization across domains. To address this, we propose a novel semantic bias-aware framework that enhances LLM-based ZCDSR by improving cross-domain alignment at both the item and sequential levels. At the item level, we introduce a generalization loss that aligns the embeddings of items across domains (inter-domain compactness), while preserving the unique characteristics of each item within its own domain (intra-domain diversity). This ensures that item embeddings can be transferred effectively between domains without collapsing into overly generic or uniform representations. At the sequential level, we develop a method to transfer user behavioral patterns by clustering source domain user sequences and applying attention-based aggregation during target domain inference. We dynamically adapt user embeddings to unseen domains, enabling effective zero-shot recommendations without requiring target-domain interactions. Extensive experiments across multiple datasets and domains demonstrate that our framework significantly enhances the performance of sequential recommendation models on the ZCDSR task. By addressing domain bias and improving the transfer of sequential patterns, our method offers a scalable and robust solution for better knowledge transfer, enabling improved zero-shot recommendations across domains.