Ok, Kerry, this is what I would do in your place:
What you want is a caseificio in Andria; they will all make burrata and other cheeses. They may not say on their website that they give tours, but I think there is a high probability that if you get in touch with them in advance, they will let you watch their process. If you are staying at a hotel or have a B&B host, you could ask them to phone a few place and ask if you could visit at the hour that they are making the cheeses (usually in the early morning). But the likelihood that they speak English is slim so that would not be a tour, but it would allow you to watch how the cheese is made. I've done this a few times, once near Alberobello and twice more in a caseificio on the main SS road in Speziale, near Savelletri. And once, I asked at my hotel and they had someone drive me over to a cheese-maker nearby....this was also near Savelletri.
So here are a few names; you can e-mail and if you get no answer, have someone phone for you a day or two in advance, not weeks ahead. It goes without saying that if you do this, you ought to buy a few cheeses from the makers.
https://montrone.net/our-artisans/?lang=en
https://caseificioolanda.it/museo-del-latte/?lang=en. (They have a "milk museum," so apparently are ok with welcoming tourists...)
https://www.caseificioperina.it/en
Those will not be organized tours, just a chance to let you watch the process.
Your other option would be to try to find a tour, which will cost a lot more but might I include transport and English speaking guide.
Here is a producer of olive oil and wine in Andria that allows visitors; they also sell a variety of jarred and tinned food items.
https://www.contespagnolettizeuli.it/visita-in-cantina/?_gl=1*6uo5hi*_up*MQ..*_ga*MzQ5MDEyOC4xNzQ1NTk4MDA0*_ga_YP5QYQL0KP*MTc0NTU5ODAwMS4xLjAuMTc0NTU5ODAwMS4wLjAuMTgxNjkxMzIwOQ..
So in order to go this route, you have to look into it and make some phone calls or, better, have an Italian-speaker call for you..... I have not been to Puglia in more than ten years but when I was there, the cheese makers were always happy to have visitors (they especially loved Americans; I don't know where you re from..). I think there now are more organized tours and visits but I still like going solo, and it's a lot less pricey.
Do you understand any Italian?
Please let us know how you fare.if you get in touch with any of those makers; they are just a few of the many you can find online by googling "caseificio Andria," or "azienda Andria."