Many relevant biological processes take place on time scales not reachable by standard all-atom computer simulations. The translocation of antibiotics through non-specific bacterial porins is an example. Microscopic effects compete to determine penetration routes and, consequently, free energy barriers to be overcome. Since bacteria can develop resistance to treatment also by reducing their antibiotic permeability, to understand the microscopic aspects of antibiotic translocation is an important step to rationalize drug design. Here, to investigate the translocation we propose a complete numerical model that combines the diffusion-controlled rate theory and a kinetic Monte Carlo scheme based on both experimental data and microscopically well-founded all-atom simulations. Within our model, an antibiotic translocating through an hour-glass-shaped channel can be described as a molecule moving on a potential of mean force featuring several affinity sites and a high central barrier. The implications of our results for the characterization of antibiotic translocation at in vivo concentrations are discussed. The presence of an affinity site close to the mouth of the channel seems to favor the translocation of antibiotics, the affinity site acting as a particle reservoir. Possible connections between results and the appearance of mutations in clinical strains are also outlined.