After you beat her tower, she'll appear in the overworld at the Desolate Church somewhat near her tower, located up in the red forest north of the Windswept Hills. She'll still be a little bitter about losing to you, and she'll have 3 quests for you to do before joining you.

1) For her first quest, she'll tell you to capture a Grizzbolt of your own, and tells you where to find one; at the #1 Wildlife Sanctuary, just south of the map. Grizzbolt is a rare spawn, so it may take some running around for a bit (and maybe killing) to get it to spawn.
-If you ALREADY have one, you don't have to worry about this part :)

2) she'll ask that you beat up 5 of the Free Pal Alliance members for her. If you need to find them, they're just a little further north of a red forest and quite a few of them can be found around the edges of the Ancient Ritual Site where Petallia is sealed.

3) For her final request, After you catch Grizzbolt and show it off, she'll ask you to find a blanket she once used as a runaway. The blanket will be in the Fort Ruins just north of the default starting area, and East of her tower.

After that, she'll decide to join up with you! Congrats, Zoe is now your firend!

Zoe and Grizzbolt are a pair and function exactly how they do in her tower fight, with her riding on top of it. They'll be inside of your Palbox and to add her to the team, you'll have to give up one of your slots for your Pals.

If you've crafted the minigun for Grizzbolt, you'll still be presented with the option to ride it and will be sitting on top of it right next to Zoe, and can still blast away as you please.

OR.............
You can also catch her in a Pal sphere :) (STRONGLY Recommend doing this after completing her quest first and getting her and Grizzbolt if you're on multi. Solo play sees her respawn, but a lot of people have been having it where she does not respawn on the server and get locked out. So far it's been mixed, others do get her to respawn. So I just suggest do all of her stuff first before attempting this. More on this in the extra section)

(Not gonna lie, I rarely go out of my way to capture humans so I completely FORGOT this was a possibility. If you catch her this way, she does use her gun!! It's bright pink and if you try to pet her, she'll pout but have hearts like a tsundere)

In regards to her respawning, I've had my friends and I do several tests on getting her to respawn after catching her in a pal sphere. We did dedicated servers and hosted multiplayer sessions each. One group on a dedicated server never got her back, but joining in on a multiplayer session, she came back after a world reset (so quitting the world and coming back in).
However, the second group repeated the same exact steps and never got her back; it has been 3 play sessions since. Honestly, I think maybe its just bugged for the second group since she's new?

As a follow up, those that have captured her, once you deploy her on base as a worker, she can STILL be spoken to as an NPC. So there is still hope there! Thanks to tommelom10 in the comment to test the idea like the merchants.