The nasal olfactory region is a potential route for non-invasive delivery of drugs directly from the nasal epithelium to the brain, bypassing the often impermeable blood-brain barrier. However, efficient aerosol delivery to the olfactory region is challenging due to its location in the nose. Here we explore aerosol delivery with bi-directional pulsatile flow conditions for targeted drug delivery to the olfactory region using a computational fluid dynamics (CFD) model on the patient-specific nasal geometry. Aerosols with aerodynamic diameter of 1 µm, which is large enough for delivery of large enough drug doses and yet potentially small enough for non-inertial aerosol deposition due to, e.g., particle diffusion and flow oscillations, is inhaled for 1.98 s through one nostril and exhaled through the other one. The bi-directional aerosol delivery with steady flow rate of 4 L/min results in deposition efficiencies (DEs) of 50.9 and 0.48% in the nasal cavity and olfactory region, respectively. Pulsatile flow with average flow rate of 4 L/min (frequency: 45 Hz) reduces these values to 34.4 and 0.12%, respectively, and it mitigates the non-uniformity of right-left deposition in both the cavity (from 1.77- to 1.33-fold) and the olfactory region (from 624- to 53.2-fold). The average drug dose deposited in the nasal cavity and the olfactory epithelium region is very similar in the right nasal cavity independent of pulsation conditions (inhalation side). In contrast, the local aerosol dose in the olfactory region of the left side is at least 100-fold lower than that in the nasal cavity independent of pulsation condition. Hence, while pulsatile flow reduces the right-left (inhalation-exhalation) imbalance, it is not able to overcome it. However, the inhalation side (even with pulsation) allows for relatively high olfactory epithelium drug doses per area reaching the same level as in the total nasal cavity. Due to the relatively low drug deposition in olfactory region on the exhalation side, this allows either very efficient targeting of the inhalation side, or uniform drug delivery by performing bidirectional flow first from the one and then from the other side of the nose.