Just leave it bent over and she will grow fine. Leaving duct tape around the wound could induce fungal/mould problems due to the moist conditions. As long as the the two parts are still attached, above and below the break, she will heal herself and grow more or less normally, apart from the bent stem. If you have kept her "standing up", making a splint (bamboo skewer/ice cream stick/twig etc) that spans the break and is held in place with soft, rubber covered wire or pipe cleaner or something similar, she will also be fine and grow normally. No need to throw her away, she has amazing powers of recovery. Make sure the "wound" is in the open air, it will be better for healing and will prevent fungal attack.
Hope this helps,.........
Organoman.