A bulge is a group of stars bunched together within a larger group, the term most often used for the central region of some disk galaxies, which protrude from the plane of the disk. The very center of such galaxies often have a central supermassive black hole (SMBH) and/or a compact stellar nucleus (hundreds of thousands or millions of stars within a parsec radius), but the bulge is a larger group of stars not nearly that dense, with dimensions in the 100s to 1000s of parsecs. The bulge can be a bar (elongated) or a pseudobulge (flat, i.e., little or no protrusion from the disk). It also can have structure within it much like galaxies, with bars and/or arms.
The Milky Way's central bulge, the galactic bulge, is presumed to be a bar, surrounding the galactic center, that includes a compact stellar nucleus and a central SMBH.