There is an entirely different rhythm to hitting the double-end bag, than any other punching bags. Heavy bags don't punch back, double-end bags do! You learn to bob and weave, slip and duck, keep your hands up and move your head. When you strike the double-end bag, it will react by moving quickly away, then rebound back right at you.
You can either wear your boxing gloves, striking mitts or hand wraps when hitting the double-end striking bag. Boxing gloves give a larger contact surface and initially may be a better choice. Work towards using just hand wraps or striking mitts.
Address the bag in your boxing stance, hands up and get ready to move. Stay light on your feet, the weight centered more towards the front of the feet.
Strike the bag and slip out of the way of the rebound. You do not have to strike with a lot of power, work on technique. Try to strike in the center of the bag at first, making the bag move directly back and straight at you. Move out of the way and then strike the bag again. Practice your slips, add footwork, move in and out, circle the bag, and mix up the punches.