Cessna 172 student pilot reported running off the end of the runway after a high speed bounced landing.

Narrative

Once I reached [the] runway I noticed that I was coming in a little fast; but didn't think it was anything to worry about. I took my power out; knowing that would slow me down; but miscalculated how much runway I would still need. I touched down on the runway; then ballooned back up which felt fine because I had done that many times before. The second time I touched down and ballooned back up I understand now that this was going to be a very complex situation. The third time I came down; I stayed on the ground and had a moment where I decided I could either try to take off and put power back in; but I might hit the lights at the end of the runway; or I could just stay on the ground and stop. In the split second decision I decided to stay on the ground as to not cause any damage to the plane and because there was not enough runway for me to make it back up. As I came speeding directly for the lights I swerved to the right and ended up in a plowed bean field behind the runway. There I was stuck in the mud and called my instructor for help. I then turned the plane off and climbed out in search of someone who could help me.