We tackle the integrated planning problem of periodic timetabling and electric vehicle scheduling, crucial for cities transitioning to electric bus fleets. Given existing timetables, we allow only minor modifications and propose an iterative solution approach that addresses the Electric Vehicle Scheduling Problem (EVSP) in each iteration. Due to the NP-hard nature of EVSP, we employ well-established heuristics and evaluate the quality of the solutions obtained. Specifically, we establish tight approximation bounds for certain iterative heuristics that first solve the Vehicle Scheduling Problem and subsequently adjust solutions to meet battery constraints. We make several key contributions: We provide general insights into heuristic solution quality, establish theoretical performance bounds, and validate these findings through a case study using real-world data from Aachen, Germany. Additionally, we employ our iterative framework to derive managerial insights for bus operators in Aachen by quantifying potential gains from adjusting the timetable to support the transition to a fully electric bus fleet.