Mobile cloud computing relieves the tension between compute-intensive mobile applications and battery-constrained mobile devices by enabling the offloading of computing tasks from mobiles to a remote processors. This paper considers a mobile cloud computing scenario in which the "cloudlet" processor that provides offloading opportunities to mobile devices is mounted on unmanned aerial vehicles (UAVs) to enhance coverage. Focusing on a slotted communication system with frequency division multiplexing between mobile and UAV, the joint optimization of the number of input bits transmitted in the uplink by the mobile to the UAV, the number of input bits processed by the cloudlet at the UAV, and the number of output bits returned by the cloudlet to the mobile in the downlink in each slot is carried out by means of dual decomposition under maximum latency constraints with the aim of minimizing the mobile energy consumption. Numerical results reveal the critical importance of an optimized bit allocation in order to enable significant energy savings as compared to local mobile execution for stringent latency constraints.