The main contribution of this paper is an algorithm for integrating motion planning and simultaneous localisation and mapping (SLAM). Accuracy of the maps and the robot locations computed using SLAM is strongly dependent on the characteristics of the environment, for example feature density, as well as the speed and direction of motion of the robot. Appropriate control of the robot motion is particularly important in bearing-only SLAM, where the information from a moving sensor is essential. In this paper a near minimum time path planning algorithm with a finite planning horizon is proposed for bearing-only SLAM. The objective of the algorithm is to achieve a predefined mapping precision while maintaining acceptable vehicle location uncertainty in the minimum time. Simulation results have shown the effectiveness of the proposed method.