Bigfoot isn't in a zoo for the same reason Amelia Erhart's plane isn't in a museum. It's out there, but no one has found it definitively yet.
As far as a zoo goes, I used to want Bigfoot in a zoo. Then, as I got older, I had second thoughts. This further struck home with me when watching this Bigfoot researcher from Bigfoots Reflection:
He said essentially: if we caught bigfoot what do we do with him? I go to the zoo and watch apes and they seem...sad.
I happen to agree with this now. I selfishly wanted Bigfoot in a zoo when I was younger. Now, it would be enough to have proof such a rare thing exists and let it be free.