Dark matter particles scattering off some target nuclei are expected to deposit very small energies in form of nuclear recoils (below 100 keV). Because of the low scintillation efficiency for nuclear recoils vs. electron recoils, in most of the scintillating targets considered in the search for dark matter, the region below 10 keVee concentrates most of the expected dark matter signal. For this reason, very low energy threshold (at or below 2 keVee) and very low background are required. This is the case of the ANAIS (Annual modulation with NaI Scintillators) experiment. A good knowledge of the detector response function for real scintillation events, a good characterization of other anomalous or noise event populations contributing in that energy range, and the development of convenient filtering procedures for the latter are mandatory to achieve the required low background at such a low energy. In this work we will present the specific protocols developed to select bulk scintillation events in NaI(Tl), and its application to data obtained with the ANAIS-0 prototype. Slight differences in time constants are expected in scintillation pulses produced by nuclear or electron recoils in NaI(Tl), so in order to analyze the effect of these filtering procedures in the case of a recoil population attributable to dark matter, data from a neutron calibration have been used.