Zero-shot cross-domain sequential recommendation (ZCDSR) enables predictions in unseen domains without the need for additional training or fine-tuning, making it particularly valuable in data-sparse environments where traditional models struggle. Recent advancements in large language models (LLMs) have greatly improved ZCDSR by leveraging rich pretrained representations to facilitate cross-domain knowledge transfer. However, a key challenge persists: domain semantic bias, which arises from variations in vocabulary and content focus across domains. This misalignment leads to inconsistencies in item embeddings and hinders generalization. To address this issue, we propose a novel framework designed to enhance 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 promotes inter-domain compactness by aligning embeddings of similar items across domains while maintaining intra-domain diversity to preserve unique item characteristics. This prevents embeddings from becoming overly generic while ensuring effective transferability. At the sequential level, we develop a method for transferring user behavioral patterns by clustering user sequences in the source domain and applying attention-based aggregation for target domain inference. This dynamic adaptation of user embeddings allows effective zero-shot recommendations without requiring target-domain interactions. Comprehensive experiments across multiple datasets and domains demonstrate that our framework significantly improves sequential recommendation performance in the ZCDSR setting. By mitigating domain bias and enhancing the transferability of sequential patterns, our method provides a scalable and robust approach for achieving more effective zero-shot recommendations across domains.