Polylactic acid (PLA)-based cylindrical membranes for the controlled release of fluorescein sodium salt (FS) were prepared by bioprinting on systems with an initial FS concentration of 0.003763 gdm−3 and 37.63 gdm−3, and the drug release process was monitored in a bath at 37 °C. Photographs, acquired at regular intervals during the process, revealed marked osmotic swelling of the polymer. Osmotic swelling consists in the enlargement of the polymer structure and due to the influx of water molecules across the membrane. The cylindrical PLA membrane starts to significantly swell once a certain threshold range is crossed. Important amounts of FS can dissolve under these radically changed circumstances, and the dissolved FS molecules are mobile enough to diffuse out of the cylinder, thus allowing drug release. As a matter of fact, in this investigation, we ascertained that polymer swelling promotes the mass transport phenomenon by altering the conditions for drug dissolution and diffusion, hence facilitating FS release after a specific lag time. Furthermore, in order to compare the release kinetics, the half-release time, t0.5, was taken into consideration. The data of this study evidence that, while increasing the initial concentration of FS by three orders of magnitude, the time parameter, t0.5, is only reduced by 5/6. In addition, the yield of the release process is drastically reduced due to the strong aggregation ability of the dye. Finally, it is demonstrated that a compressed exponential kinetic model fits the experimental data well despite the varying physical conditions.