Knowledge Graphs (KGs), as structured knowledge bases that organize relational information across diverse domains, provide a unified semantic foundation for cross-domain recommendation (CDR). By integrating symbolic knowledge with user-item interactions, KGs enrich semantic representations, support reasoning, and enhance model interpretability. Despite this potential, existing KG-based methods still face major challenges in CDR, particularly under non-overlapping user scenarios. These challenges arise from: (C1) sensitivity to KG sparsity and popularity bias, (C2) dependence on overlapping users for domain alignment and (C3) lack of explicit disentanglement between transferable and domain-specific knowledge, which limit effective and stable knowledge transfer. To this end, we propose KGBridge, a knowledge-guided prompt learning framework for cross-domain sequential recommendation under non-overlapping user scenarios. KGBridge comprises two core components: a KG-enhanced Prompt Encoder, which models relation-level semantics as soft prompts to provide structured and dynamic priors for user sequence modeling (addressing C1), and a Two-stage Training Paradigm, which combines cross-domain pretraining and privacy-preserving fine-tuning to enable knowledge transfer without user overlap (addressing C2). By combining relation-aware semantic control with correspondence-driven disentanglement, KGBridge explicitly separates and balances domain-shared and domain-specific semantics, thereby maintaining complementarity and stabilizing adaptation during fine-tuning (addressing C3). Extensive experiments on benchmark datasets demonstrate that KGBridge consistently outperforms state-of-the-art baselines and remains robust under varying KG sparsity, highlighting its effectiveness in mitigating structural imbalance and semantic entanglement in KG-enhanced cross-domain recommendation.