The problem of designing a set of routes with minimum cost to serve a collection of customers with a fleet of vehicles is a fundamental challenge when the number of customers to be dropped or picked up is not known during the planning horizon. The purpose of this paper is to develop a vehicle routing Problem (VRP) model that addresses stochastic simultaneous pickup and delivery in the urban public transport systems of Addis Ababa city Bus Enterprise, in Ethiopia. To this effect, a mathematical model is developed and fitted with real data collected from Anbessa City Bus Service Enterprise (ACBSE) and solved using Clark-Wright saving algorithm. The form-to-distance is computed from the data collected from Google Earth and the passenger data from the ACBSE. The findings of the study show that, the model is feasible and showed an improvement as compared to the current performances of the enterprise. It has shown that, an improvement on the current number of routes (number of buses used) and the total kilometer covered. The average performances of the model show that on average 6.48 routes are required to serve passenger demands of 271 and on average the simulation run was performed with 0.40 seconds of CPU time. During this instance, the average distance traveled by the vehicles in a single trip is 552.92kms.