Id say this is a good example for showing people what the real difference is between the differing ideologies.A Libertarian... now that is a difficult cat to pin down... you seem to have A version you wish to use but there are a many Libertarian types out there as there are Libs or CONs.
You warp the facts on the ground. First you forget the range wars where early ranchers thought they owned all the land they could use, and not pay anything for that use. As territories the Federal Government ran the lands, hence had first claim before statehood.
Then you forget as the West was settled, to be fair to everyone, you either bought the land to use or rented it from the unassigned lands. many cattle barons were outraged they couldn't run cattle wherever they felt like it... but at least they now knew how the early Spanish settlers felt when their 'royal deeds' were ignored by the supplanting Anglos...
You obviously don't know the BLM, it isn't a huge bureaucracy, but quite under-strength and relies on the honor system for land management. Bundy has not paid for YEARS, a very small rent compared to if he wanted to use private land.
The Nevada cattleman's association, not a Lib group by any means hasn't sided with Bundy because they know it isn't fair for one rancher to break the law and the others obey it.
I would opine a Libertarian would say, min gubmint yes, but no gubmint is worse. Bundy wants NO Gubmint. if we all can't run cattle on public lands rent free and anyplace we want why should a very select few get that 'right'??? this was the argument as the Homestead act settled the west after statehood. free range was over.
I'd say a Libertarian would say the public lands belong to everyone and not anyone in particular, their safeguarding belongs to the Federal Gubmint that uses a series of LOCAL offices to manage the lands for us all.