Searching for adequate and effective compounds displaying antimicrobial activities, especially against Gram-positive bacteria, is an important research area due to the high hospitalization and mortality rates of these bacterial infections in both the human and veterinary fields. In this work, we explored (E)-4-amino-3-((3,5-di-tert-butyl-2-hydroxybenzylidene)amino) benzoic acid (SB-1, harboring an intramolecular hydrogen bond) and (E)-2-((4-nitrobenzilidene)amino)aniline (SB-2), two Schiff bases derivatives. Results demonstrated that SB-1 showed an antibacterial activity determined by the minimal inhibitory concentration (MIC) against Staphylococcus aureus, Enterococcus faecalis, and Bacillus cereus (Gram-positive bacteria involved in human and animal diseases such as skin infections, pneumonia, diarrheal syndrome, and urinary tract infections, among others), which was similar to that shown by the classical antibiotic chloramphenicol. By contrast, this compound showed no effect against Gram-negative bacteria (Klebsiella pneumoniae, Escherichia coli, and Salmonella enterica). Furthermore, we provide a comprehensive physicochemical and theoretical characterization of SB-1 (as well as several analyses for SB-2), including elemental analysis, ESMS, 1H and 13C NMR (assigned by 1D and 2D techniques), DEPT, UV-Vis, FTIR, and cyclic voltammetry. We also performed a computational study through the DFT theory level, including geometry optimization, TD-DFT, NBO, and global and local reactivity analyses.