We present a novel approach to tracking of flexible bronchoscopes by modeling the output as spatially continuous over time. Bronchoscopy is a widespread clinical procedure for diagnosis and treatment of lung diseases and navigation systems are highly needed. Tracking of the bronchoscope can be regarded as a deformable registration problem. In our approach we use hybrid image-based and electromagnetic tracking, and the bronchoscope pose relative to CT data is interpolated using Catmull-Rom splines for position and SLERP for orientation. We evaluate the method using ground truth poses manually selected by experts, where mean inter-expert agreement was determined as 1.26 mm. For four dynamic phantom data sets, the accuracy of our method is between 4.13 and 5.93 mm and shown to be equivalent to previous methods. We significantly improve inter-frame smoothness from 2.35-3.08 mm to 1.08-1.51 mm. Our method provides a more realistic and physically plausible solution with significantly less jitter. This quantitative result is confirmed by video output, which is much more consistent and robust, with fewer occasions of tracking loss or unexpected movement.