You would be beating a dead horse in Colorado.
Our state lands are all leased for 5-10 years. They post a list of expiring leases in the county court houses some time before the lease is up for remewal.
If you bid on one, and you are the highest bidder, the existing leaseholder has the right to match your offer and retain the lease - even though he didn't bid on it. Also, you would be compelled to purchase whatever leasehold improvements are on the lease from the current leaseholder (such as windbreaks, fences, tanks water systems, etc. The process is quite low-key and most folks don't even know it is going on.
By the way, all the rentals are determined from private leases in the state. The rentals would be the private lease rate less 35% for fencing and water. I think we are paying about $9.00 per animal unit per month which would be the equivalent of about $14.00 for private leases.
On top of that, the state determines the stocking, rate allowing so many AUM's per year. Our lease is 640 acres and we are allowed 192 AUM's per year. For this we pay about $1,900 per year.
In dry years, we are not able to get that much grazing out of it so we eat the loss. Also, the county had discovered they can tax the "possessory interest" of the leasholder - levying property taxes on state owned land.
If this seems discouraging, the State periodically inspects the lease for overgrazing, pest control, etc. etc. etc.
Last year, they found a few prairie dogs on our lease and threatened to cut the lease term if they were not controlled. Of course, in a "green" state, you can't just go around killing these lovable creatures!!!
We do, anyway.
The advantage for us is that the state land is in the middle of our ranch and would be a problem if someone else ran cattle on it.
Also, a lot of state trust land is checkerboarded in private land on larger ranches and the land is not fenced off. If you were to acquire one of these leases, you would have to build fences, provide water and somehow make the guy whose land you have to cross to get to your lease happy - not likely since he lost the lease!! (Our state lease has no indigenous water so we water it by pipeline. If we lost the lease, no water. You could drill a well, but its about 4500 feet to water and that water is non-potable.)
Almost forgot - Colorado retains the hunting rights for most state land leases so they presumably could turn hunters loose on your lease during hunting season. I don't think this has come up, though. Our state lease is not the end of the world, but is just a mile or so short.
If you still have your heart set on this, you can get a list of lessees and buy them out - pay them cash money for their lease. The last one I saw for sale here was $35.00 per acre - about 15-20 years rental - and you still would have to pay the state annually.