Unfortunately not. In order to bounce up energy must be supplied. You could get this energy back when you fall in theory but in reality you’d rapidly stop bouncing.
If it did work, any object that bounced once on a trampoline would uncontrollably bounce higher each time until thr trampoline broke or object bounced into space!
You just can’t get energy from nothing 🙁
However if you mean powering something by bouncing then yes you can! Some watches are charged by being shaken and moved using little crystals that generate energy when struck. The same idea could be used and I think it’s part of the current development of smart clothing that makes small amounts of electricity when you move.