A bandage dispenser has a mounting strip supporting a plurality of partially overlapping bandage packages. Each package individually wraps a bandage. Each bandage package has a bifurcated opening, with one half of the bifurcated opening bonded to the mounting strip and the second half of the bifurcated opening folded away from the mounting strip to facilitate manual grasping. A person one-handedly grasps the second half of the bifurcated opening and pulls away from the mounting strip to open the bandage package. Using the same single hand, the person may release the bifurcated opening, and then grasp and remove the sterile bandage from the package. Once the bandage has been applied, a person may again use a single hand to finish tearing the bandage package from the mounting strip, revealing the next bandage package bifurcated opening. Optional pockets provide tactile feedback and reduce the chance of accidentally spilling a bandage.