Thanks for writing in.
Any cut will bleed for a while before the clotting mechanism of the body stops the bleeding. It is good that you applied antiseptic wipe and bandaged the wound. You could have applied ice cubes to stop the bleeding. There is no need to do it now because you have put bandage. You can continue to apply some pressure over the finger for sometime. Please do to allow water to enter the wound. Keep it dry should it get wet unintentionally. You an take a tetanus
toxid shot if not immunised earlier.
Hope it helps