Bronchoscopic navigation relies on registering endoscopic video to a preoperative CT scan, but respiratory motion deforms the airway by 5-20 mm, creating CT-to-body divergence that limits localization accuracy. In practice, this is mitigated through breath-hold protocols, which attempt to match the intraoperative anatomy to a static CT, but are difficult to reproduce and disrupt clinical workflow. We propose to eliminate the need for breath-hold protocols by leveraging patient-specific respiratory modeling. Paired inhale-exhale CT scans, already acquired for planning, implicitly define the patient-specific deformation space of the breathing airway. By registering these scans, we reduce respiratory motion to a single scalar breathing phase per frame, constraining all reconstructions to anatomically observed configurations. We embed this representation within a mesh-anchored Gaussian splatting framework, where a lightweight estimator infers breathing phase directly from endoscopic RGB, enabling continuous, deformation-aware reconstruction throughout the respiratory cycle without breath-holds or external sensing. To enable quantitative evaluation, we introduce RESPIRE, a physically grounded bronchoscopy simulation pipeline with per-frame ground truth for geometry, pose, breathing phase, and deformation. Experiments on RESPIRE show that our approach achieves geometrically faithful reconstruction, over 20x faster training, and 1.22 mm target localization accuracy (within the 3mm clinically relevant tolerances) outperforming unconstrained single-CT baselines. Please check out our website for additional visuals: https://asdunnbe.github.io/RESPIRE/