This work addresses a route planning problem constrained by a bus road network that includes the schedules of all buses. Given a query with a starting bus stop and a set of Points of Interest (POIs) to visit, our goal is to find an optimal route on the bus network that allows the user to visit all specified POIs from the starting stop with minimal travel time, which includes both bus travel time and waiting time at bus stops. Although this problem resembles a variant of the Traveling Salesman Problem, it cannot be effectively solved using existing solutions due to the complex nature of bus networks, particularly the constantly changing bus travel times and user waiting times. In this paper, we first propose a modified graph structure to represent the bus network, accommodating the varying bus travel times and their arrival schedules at each stop. Initially, we suggest a brute-force exploration algorithm based on the Dijkstra principle to evaluate all potential routes and determine the best one; however, this approach is too costly for large bus networks. To address this, we introduce the EA-Star algorithm, which focuses on computing the shortest route for promising POI visit sequences. The algorithm includes a terminal condition that halts evaluation once the optimal route is identified, avoiding the need to evaluate all possible POI sequences. During the computation of the shortest route for each POI visiting sequence, it employs the A* algorithm on the modified graph structure, narrowing the search space toward the destination and improving search efficiency. Experiments using New York bus network datasets demonstrate the effectiveness of our approach.