ANSWER
C. Some of her initial energy has been transferred to potential energy in the bungee cord.
EXPLANATION
A quick diagram of this situation may help us understand the problem better,
When the bungee jumper stops bouncing up and down - in other words, she is at rest again, her energy is not zero. So, not all of her initial energy was transformed into other types of energy.
When we jumped, her potential energy was transformed into kinetic energy and spring potential, then converted to potential energy again, and so on until she stopped.
Hence, when she stopped bouncing she regained a part of her initial energy as gravitational potential energy, but some of her initial energy has been transferred to potential energy in the bungee cord.
