The Galactic bulge region is a rich host of variable high-energy point sources. Since 2005, February 17 we are monitoring the source activity in the Galactic bulge region regularly and frequently, i.e., about every three days, with the instruments onboard INTEGRAL. Thanks to the large field of view, the imaging capabilities and the sensitivity at hard X-rays, we are able to present for the first time a detailed homogeneous (hard) X-ray view of a sample of 76 sources in the Galactic bulge region. We describe the successful monitoring program and show the first results from the start of the monitoring up to 2006, April 21, i.e., for a period of about one and a half year, during three visibility seasons. We focus on the short (hour), medium (month) and long-term (year) variability in the hard X-ray bands, i.e., 20-60 keV and 60-150 keV. When available, we discuss the simultaneous observations in the soft X-ray, 3-10 keV and 10-25 keV, bands. Almost all the sources in the Galactic bulge region we detect in the 20-60 keV and 60-150 keV bands are variable. During the last two and a half weeks of the third visibility season most of the known persistent (hard) X-ray sources in the Galactic Center region were not detected. Of our sample of sources, per visibility season we detect 32/33 sources in the 20-60 keV band and 8/9 sources in the 60-150 keV band above a signal to noise of 7. On average, we find per visibility season one active bright (> 100 mCrab, 20-60 keV) black-hole candidate X-ray transient and three active weaker (<=sssim25 mCrab, 20-60 keV) neutron star X-ray transients. Most of the time a clear anti-correlation can be seen between the soft and hard X-ray emission in some of the X-ray bursters. Hard X-ray flares or outbursts in X-ray bursters, which have a duration of the order of weeks are accompanied by soft X-ray drops. On the other hand, hard X-ray drops can be accompanied by soft X-ray flares/outbursts. During the course of our program we found a number of new sources, IGR J17354-3255, IGR 17453-2853, IGR J17454-2703, IGR J17456-2901b, IGR J17536-2339, and IGR J17541-2252. We report here on some of the high-energy properties of these sources. The high-energy light curves of all the sources in the field of view, and the high-energy images of the region, are made available through the WWW, as soon as possible after the observations have been performed, at http://isdc.unige.ch/Science/BULGE/.