Wounds heal best when they’re kept moist, (something tattoo artists have known about for a long time, as they always suggest keeping lotion on a healing tattoo) and traditional gauze bandaging actively dries out wounds. This prevents effective healing and causes additional scarring.
Stop the bleeding, and then smear a bit of Vaseline on top of the wound before putting a bandage on to cover it. The Vaseline will prevent the bandage from drying out the wound, allowing it to heal faster and with less scarring.