Operating unmanned aerial vehicles (UAVs) over inhabited areas requires mitigating the risk to persons on the ground. Because the risk depends upon the flight path, UAV operators need approaches that can find low-risk flight paths between the mission's start and finish points. Because the flight paths with the lowest risk could be excessively long and indirect, UAV operators are concerned about the tradeoff between risk and flight time. This paper presents a risk assessment technique and bi-objective optimization methods to find low-risk and time (flight path) solutions and computational experiments to evaluate the relative performance of the methods (their computation time and solution quality). The methods were a network optimization approach that constructed a graph for the problem and used that to generate initial solutions that were then improved by a local approach and a greedy approach and a fourth method that did not use the network solutions. The approaches that improved the solutions generated by the network optimization step performed better than the optimization approach that did not use the network solutions.