There is no adverse possession against the government, except in very limited circumstances, none of which apply in the Bundy matter. If Bundy is planning on an adverse possession case against the United States, he's getting very bad legal advice, like those folks who claim they can file a document with the County and convert to Allodial Title to get out of paying property taxes.
What does seem to apply, is the early history of the use of the Public Domain in the frontier West. The first users of the water have a senior right to the water, to the exclusion of 'downstream' users. Bundy ancestors put cattle on the open range around 1877, and gained a right to water they needed to keep the cattle alive. With that right, they also get a grazing right, to keep the cattle alive. You can't have one without the other, it seems. Under state law, the rights would be legally vested, and some Federal case law says the same thing. It gets murky with the rise of the Grazing Service (now BLM), Allotments, permits, fees, etc., and 19th-century purchases of Allotments and the rights that come with such ownership of partial fee estates. Bundy apparently purchased such an Allotment around 1890 or so, and these things have morphed over time into Grazing Permits, Animal Unit Months, etc., the modern system of administering ranching uses of the public domain.
Add to that modern regulations, fees, case law concerning water rights where Indian needs and wildlife needs are at issue, the fact that the US owns 90% of the land area of Nevada, far more than any other state, and what is legal and what is correct is very convoluted and there are no black and white answers to either the positions held by Bundy or the United States. Throw in the politicization of one or both sides of the matter, and it gets a whole lot worse.
I watched a couple of protestor videos taken at the protest site, there was without doubt the real potential for serious violence, and the BLM was wise to back away and end it for now. I think people on both sides were stupid to set up the situation that resulted in the confrontations. While the citizens who just showed up to protest are within their rights, the BLM managers who planned this 'event' have some explaining to do before Congress, and some militia organizers have some explaining to do, as well. There seemed to be a 'provoke me' calculus on both sides, and people could have been in the middle of a shootout very easily.