The delayed ion extraction method has been used to study characteristics of the initial velocity distributions of positive and negative ions produced simultaneously by laser desorption/ionization (LDI) from non-impacted single aerosol polymeric particles, using a bipolar time-of-flight (TOF) instrument (LAMPAS 2). Due to the geometry of the setup and the characteristics of the ablation process, only the projections of the velocities on the axis of the mass spectrometer can be directly studied. Additionally, since the mean initial velocity under these conditions should be close to zero, it was necessary to extend the method by taking into account higher order contributions of the velocity distribution. Theoretical expressions for these higher order terms are presented and discussed. The bipolar characteristics of the instrument permit evaluation and treatment of a possible instrumental artifact caused by small inclinations of the ionizing laser with respect to the ideal incidence direction. Results of a number of experiments are presented and discussed in relation to the theoretical expressions presented, and to possible ablation scenarios. Evidence pointing out that, under our experimental conditions, only partial ablation of the latex particles occurs was obtained. The variance of the distribution of the projection of the initial velocities can be directly estimated from these results. By assuming that the total initial velocities of the ions are developed completely according to a single-temperature adiabatic expansion mechanism, temperatures of approximately 50 K/Da can be assigned to the ion clouds from the variance estimations. If a two-temperature model is used, a radial temperature of about 100 K/Da results. These values are in reasonable agreement with results for polymer ablation from the literature.