Faculty often wish to allow for guided exploration or a deeper view of at least one topic in a bridge course. However, when the time allotted to such a course is only seven to ten weeks, it can be difficult to avoid moving quickly from one topic to another--leaving little opportunity for students to see a unified context in which the structures and proof skills might actually be used. We describe three years of experience in supplementing a more traditional bridge course. Our strategy was a low-pressure "notebook" for guided exploration in a specific structure (graphs). This provided a unified environment for students to attempt various proof strategies, but (when properly managed and prepared) did not add appreciably to the pace or stress of courses--especially important when time is short! (Contains 1 figure.)