Once IV thethers onto the ledge while I'm holding it, what are my best options? I usually wait for IV to come off the ledge and punish with bair, but he always seems to fade back to ledge when I go for this.
Any insight as to what's the optimal punish?
Since Fox is so fast (and if you're under 100%), you can probably do regular get up on reaction to turn around and UpSmash. Bair is pretty good, and Uair is good as a read. Mainly, you want Ivy to pick a bad option (which is pretty much anything if you're holding the ledge), and then punish it in some way with Fox's fast speed. Remember she get's two tethers before it fails, so if Ivy is fading back consistently, just wait on the ledge. Even if she get's up first, you're still Fox, and can get up quickly to punish.
On a side note about approaching, be careful about Crouch Canceling, as Ivy has a lot of good options for CCing. Dtilt can pop you up for a combo, and jab can knock you down into grab, tech chase, or other things that Fox definitely doesn't want. To deal with that, I recommend using Dair for your approach if you notice they CC a lot (like my friend does, who is really good at that). Make sure to mix it up though, as doing the same thing will inevitably have a counter to it. Just remember "Don't get hit," since Ivy can punish you super hard, and being off stage is terrible for you.
Bait and punish. Bait and punish. Bait and punish.