Damaged bumper - insurance or just pay out of pocket?

i foolishly reversed into a neighbours car, stratching her bumper - repaint job needed for her bumper. However, mine is damaged, the corner of the bumper is exposed and dented. Is it worth paying out of pocket to fix or insurance? Relatively new cars. For a temp measure i was thinking of duct tape on the gap, just for when i am travelling on the M4 too, or just drive around?