Exoplanet discoveries since the mid-1990's have revealed an astounding diversity of planetary systems. Studying these systems is essential to understanding planetary formation processes, as well as the development of life in the universe. Unfortunately, humanity can only observe limited aspects of exoplanetary systems by telescope, and the significant distances between stars presents a barrier to in situ exploration. In this study, we propose an alternative path to gain insight into exoplanetary systems: Bridge, a mission concept design to fly by an interstellar object as it passes through our solar system. Designed as a New Frontiers-class mission during the National Aeronautics and Space Administration (NASA) Planetary Science Summer Seminar, Bridge would provide a unique opportunity to gain insight into potential physical, chemical, and biological differences between solar systems as well as the possible exchange of planetary materials between them. Bridge employs ultraviolet/visible, near-infrared, and mid-infrared point spectrometers, a visible camera, and a guided impactor. We also provide a quantitative Monte Carlo analysis that estimates wait times for a suitable target, and examines key trades between ground storage and a parking orbit, power sources, inner versus outer solar system encounters, and launch criteria. Due to the fleeting nature of interstellar objects, reaching an interstellar object may require an extended ground storage phase for the spacecraft until a suitable target is discovered, followed by a rapid response launch strategy. To enable rapid response missions designed to intercept such unique targets, language would need to be added to future NASA announcements of opportunity such that ground storage and rapid response would be allowable components of a proposed mission.