Temporal graph learning is crucial for dynamic networks where nodes and edges evolve over time and new nodes continuously join the system. Inductive representation learning in such settings faces two major challenges: effectively representing unseen nodes and mitigating noisy or redundant graph information. We propose GTGIB, a versatile framework that integrates Graph Structure Learning (GSL) with Temporal Graph Information Bottleneck (TGIB). We design a novel two-step GSL-based structural enhancer to enrich and optimize node neighborhoods and demonstrate its effectiveness and efficiency through theoretical proofs and experiments. The TGIB refines the optimized graph by extending the information bottleneck principle to temporal graphs, regularizing both edges and features based on our derived tractable TGIB objective function via variational approximation, enabling stable and efficient optimization. GTGIB-based models are evaluated to predict links on four real-world datasets; they outperform existing methods in all datasets under the inductive setting, with significant and consistent improvement in the transductive setting.