Die a lot.
No, but seriously, some tips:
-Don't do anything with commitment offstage. Bair (properly spaced) beats every recovery option you have. Up Air's falling hitbox also spikes, so any Ivy with Ness experience will use it to snipe low, close to the stage recoveries. I mean, there's a hundred other ways Ivy can ruin your day offstage, but I don't have time to list them all. Just don't go out there unless you're 100% sure you can kill her.
-Ivy has a throw mix up with dthrow and uthrow into UpB. Correct DI for dthrow is down-away, Correct DI for uthrow is straight back. DIing for the wrong one will cause all of your cookies to be eaten. Of course if Ivy has SolarBeam charged, dthrow will net Ivy one or the other pretty much guaranteed. So in that situation, don't get grabbed. =l
-For the love of god, ban Yoshi's Island Brawl.
For what it's worth, I think this is a 6-4 counter to Ness. He's got the tools to win, but he has to play super patient, and can afford to make far fewer mistakes than Ivy.