All versions of Zappa want to be on the ground. You don't get free jump/airdash ins, this applies to practically every single character in the game. You either wait for the opportunity to present itself (like if they do a slow move) or you set it up (like off a knockdown or a followup from a GhostThrow FRC or Dog Attack, etc)
Naked Zappa and Sword Zappa really, really don't ever want to leave the ground, without reason or setup. Ghost Zappa may jump just to get a different angle for a GhostThrow. Dog Zappa can do whatever he wants as long as the Dog is nearby to cover him. Roah Zappa, I'd call you an idiot for jumping, but he does such obscene damage that you can get away with a smart jump here and there. But why would you want to jump when Raoh has such strong zoning from the ground?
But, if you want to jump with Naked or Sword Zappa, setup your jump arc to make anti-airing you trickier. With both, you generally use j.HS. With the Sword, you can do tricks to have the sword lag far behind you, letting you do safer crossups.