I have found that the most accurate way to find where public land ends and private land starts is to go to the local BLM office...preferably one that is as close as possible to the area you wish to hunt...and get maps. You should talk to the BLM officer, telling him what you want to do and ask him to bring you up to date on ranchers/land owners who might have recently purchased government land. It is also always a good idea to scout the territory to see if there are any owner's homes or ranches in the surrounding area. If so, tell them you will be hunting on BLM land and that you won't be trashing the place up, shooting cattle, etc. You want to get them on your side...even though you won't be (hopefully) hunting on their property.
You want to get owners on your side by at least telling them you are there and getting acquainted with them. If they hear gunshots from a hunter who has not at least informed landowners of their presence, those landowners might not know whether or not hunters are shooting BLM property or private property. It is all a matter of courtesy. I have never had a problem with landowners. I introduce myself, tell them I am an experienced hunter, member of the NRA, Varmint Hunter's Association, and that I am well aware of cattle, irrigation pipes, etc. The worst they do is to say "no," but I haven't had this experience so far.
If you happen to harvest an animal, it is always a courtesy to share some of the meat with the rancher. Often, they will be delighted and it will be easier for them to welcome you back the following year.