It doesn't sound like Bundy owns anything. I understand that ownership rights can be divided. But like you, I don't know what Bundy owns. Does he own water rights. He was leasing grazing rights for a while. I don't think most people know. I think they are reacting emotionally. And they are assuming the courts are flawed.
At the least he owned his own property, which I understand from the various articles to be 600 acres. Beyond that, he had, at least until 1993, grazing rights for a large surrounding area of land. Part of the issue is whether those rights, which can be inherited and sold separate from the land itself, can be unilaterally taken back or altered - such as the BLM altering the terms to what amounted to one cow/calf pair per 1.3 square miles of range.