Well, I didn't recognize how good our jab could be against some aerial approaches - with that in mind, our jab doesn't have THAT much range.
While it's been mentioned above that Ness's moves aren't safe on Charizard's shield, I think it's sound to argue that he's better able to hover out of Charizard's range anyways - Flamethrower is relatively unsafe against Ness, for one, since he can just absorb it with PSI Magnet. Charizard's Flamethrower range lets him pester enemies as he tries to approach, or at least stop them from hovering just out of his range, sort of like Bowser's Fire Breath, and without being able to use it relatively safely he's left without an approach option in his specials, left to his normal moves and grabs. Ness on the other hand is faster than Charizard overall, has PK Fire to keep Charizard from moving forward on the ground, and can do multiple aerials as opposed to Charizard's usual one, making him better suited to punish Charizard, in my opinion, if one of them messes up. Also, Charizard's grab range isn't a ridiculous amount larger than Ness's, although it is much much more helpful within a shield. What I'm getting at is that while Ness's options against our shield are limited, so are our options to stop him from hovering practically right next to it...
With that all being said, Ness will have it rough against a Charizard who knows the match-up, even if he knows it himself. His options ARE limited. In a way, Ness has to play like Charizard - capitalizing on mistakes and reading the actions of the enemy - to beat Charizard. Overall, I would suggest that we're relatively forced to be lame here, as despite our main aerials being able to autocancel, Ness is just quick and used to approaching from the air regardless.
Also, I'm interested to see how this match-up would be different when platforms are involved, as the above that I've said could become irrelevant there.