Cross-domain sequential recommendation (CDSR) alleviates interaction sparsity by jointly modeling user behaviors across multiple domains. While current studies have made some progresses, they still neglect two issues that severely impact recommendation performance: (i) ignoring domain-specific interaction frequencies and interest decay rates at identical time intervals; (ii) treating semantic preferences as time-invariant during cross-domain transfer. To address these, we propose a novel framework that bridges Behavior and Semantics for Time-aware Cross-Domain Sequential Recommendation (BST-CDSR ). Specifically, we design a behavioral preference evolution module that decouples long-term interests and short-term intentions, and models continuous-time preference via a neural ordinary differential equation (ODE) with event-driven updates. Additionally, to capture time-aware semantic preferences, we introduce a temporal counterfactual-enhanced semantic generator that discretizes temporal interval tokens and leverages large language models (LLMs) to extract robust temporal semantics, where counterfactual perturbations enhance the time sensitivity of semantic preferences. Furthermore, we propose a time-preference guided domain transfer module to adaptively control transfer weights and mitigate negative transfer. Extensive experiments on real-world datasets demonstrate that BST-CDSR consistently outperforms baselines.