HEX-P is a probe-class mission concept that will combine high spatial resolution X-ray imaging (<10 '' FWHM) and broad spectral coverage (0.2-80 keV) with an effective area far superior to current facilities' (including XMM-Newton and NuSTAR). These capabilities will enable revolutionary new insights into a variety of important astrophysical problems. We present scientific objectives and simulations of HEX-P observations of the Galactic Center (GC) and Bulge. We demonstrate the unique and powerful capabilities of the HEX-P observatory for studying both X-ray point sources and diffuse X-ray emission. HEX-P will be uniquely equipped to explore a variety of major topics in Galactic astrophysics, allowing us to 1) investigate broad-band properties of X-ray flares emitted from the supermassive black hole (BH) at Sgr A* and probe the associated particle acceleration and emission mechanisms; 2) identify hard X-ray sources detected by NuSTAR and determine X-ray point source populations in different regions and luminosity ranges; 3) determine the distribution of compact object binaries in the nuclear star cluster and the composition of the Galactic Ridge X-ray emission; 4) identify X-ray transients and measure fundamental parameters such as black hole spin; 5) find hidden pulsars in the Galactic Center; 6) search for BH-OB binaries and hard X-ray flares from young stellar objects in young massive clusters; 7) measure white dwarf (WD) masses of magnetic CVs to deepen our understanding of CV evolution and the origin of white dwarf magnetic fields; 8) explore primary particle accelerators in the GC in synergy with future TeV and neutrino observatories; 9) map out cosmic-ray distributions by observing non-thermal X-ray filaments; 10) explore past X-ray outbursts from Sgr A* through X-ray reflection components from giant molecular clouds.