Onset of the oscillatory thermocapillary convection in a half-zone liquid bridge is known to be sensitive to heat transfer at free surface of the liquid bridge and the ambient air motion. The effect of the heat transfer through the free surface upon the onset of the transition mechanism and three-dimensional nature of the oscillatory flow, however, is not yet fully understood. In the present study, the thermal fluid behavior of the ambient gas and its effect upon the criticality were investigated experimentally and numerically. In the experiment, flows in the liquid bridge and the ambient air were visualized by suspending tracer particles in both fluids. Volume of the ambient air region was adjusted by placing two partition disks perpendicular to the liquid bridge. The onset of oscillation depended on the distance between the partition disks; the critical Marangoni number increased with the decreasing distance. Three-dimensional simulation of the liquid bridge and the ambient air has been performed by the finite difference method in order to determine the onset of the oscillation. The present calculations demonstrate significant influence of the heat transfer at the free surface on the onset of oscillation. The results of calculations yield a good agreement with the experimental critical values.