"jump wildly" is correct and usable in written English.
You can use it when you want to describe (in a metaphorical or literal sense) an action of jumping in an exaggerated or uncontrolled manner. For example: The music was so loud that it made her jump wildly with excitement.
The night ended with Rihanna's "We Found Love," which had the dance floor jumping wildly.
But as his 18-1 long shot was repelling the deep-stretch charge of the race favorite, Outofthebox, Hurley began jumping wildly.
Past an initial welcome home that finds Lady M. jumping wildly into her hubby's loving arms and receiving an affectionate pat on the derrière, a growing estrangement between this murderous couple leaves little room for cuddling.
Those who stood -- reporters, photographers, police officers and random others -- blew on their fingers, rubbed their arms madly and jumped wildly, movements that seemed fitting when Willie Colón began to play salsa.
Talese writes, "One month before, during a pregame exhibition at Old-Timers' Day,... DiMaggio had hit a pitch into the left-field seats, and suddenly thousands of people had jumped wildly to their feet, joyously screaming — the great DiMaggio had returned; they were young again; it was yesterday".
It's hopelessly bad at the kind of statistical thinking often required for good decisions, it jumps wildly to conclusions and it's subject to a fantastic suite of irrational biases and interference effects (the halo effect, the "Florida effect", framing effects, anchoring effects, the confirmation bias, outcome bias, hindsight bias, availability bias, the focusing illusion, and so on).
In any case the rest of the mix jumps wildly yet smoothly from one house offshoot to another, finding space for Rhythm Syndicate's brassy disco track, "Brazilian Affair," Samba La Casa's fierce "Friday Marshmallow" (featuring Chantelle, who adds ecstatic yawps), and "Cuero Na Ma," a Latin drum track starring the percussionist and singer Ray Diaz.
You think you might hear a hint of xylophone as the the bass drops from above the trees and all the elves start jumping wildly.
