The number of stars observed by the Optical Gravitational Lensing Experiment (OGLE) project in the Galactic bulge offers an invaluable chance to study RR Lyrae stars in a statistical manner. We used data of 3141 fundamental-mode RR Lyrae stars showing the Blazhko effect observed in OGLE-IV to investigate a possible connection between modulation amplitudes and periods, light curve, and pulsation characteristics. We found that there is no simple monotonic correlation between any combination of two parameters concerning the Blazhko and pulsation amplitudes, periods, and the shape of the light curves. There are only systematic limits. There is a bottom limit of the modulation period with respect to the pulsation period. We also found that the possible range of modulation amplitudes decreases with increasing pulsation period, which could point towards that the Blazhko effect is suppressed in cooler, larger, more luminous, and less metal abundant bulge RR Lyrae stars. Our investigation revealed that the distribution of the modulation periods can be described with two populations of stars with the mean modulation periods of 48 and 186d. There is a certain region with a low density of the modulated stars, which we call the Blazhko valley, in the pulsation period-modulation period plane. Based on the similarity of the modulation envelopes, basically every star can be assigned to one of six morphological classes. The double modulation was found in 25 per cent of the studied stars. Only 6.3 per cent of modulated stars belong to the Oosterhoff group II.