We present the first paper of a series focused on the Blazhko effect in RR Lyrae type stars pulsating in the fundamental mode, that are located in the Galactic bulge. A~comprehensive overview about the incidence rate and light-curve characteristics of the Blazhko stars is given. We analysed 8,282 stars having the best quality data in the OGLE-IV survey, and found that at least $40.3$,% of stars show modulation of their light curves. The number of Blazhko stars we identified is 3,341, which is the largest sample ever studied implying the most relevant statistical results currently available. Using combined data sets with OGLE-III observations, we found that 50,% of stars that show unresolved close peaks to the main component in OGLE-IV are actually Blazhko stars with extremely long periods. Blazhko stars with modulation occur preferentially among RR Lyrae stars with shorter pulsation periods in the Galactic bulge. Fourier amplitude and phase coefficients based on the mean light curves appear to be substantially lower for Blazhko stars than for stars with unmodulated light curve in average. We derived new relations for the compatibility parameter $D_{m}$ in $I$ passband and relations that allow for differentiating modulated and non-modulated stars easily on the basis of $R_{31}$, $phi_{21}$ and $phi_{31}$. Photometric metallicities, intrinsic colours and absolute magnitudes computed using empirical relations are the same for Blazhko and non-modulated stars in the Galactic bulge suggesting no correlation between the occurrence of the Blazhko effect and these parameters.
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