Check out the Bureau of Land Management. They have a website that deatails a lot of differnet regulations. They also offer some sort of "Omni Pass" for about $80, I heard. You can get into ALL National/State Parks, BLM properties, etc. Essentially, any publicly owned land in the country. All nice and official like. Worth the 80 bones if authorities try and beef with you traveling out in the world. Watch out for DNR/Park Ranger types. They have a little bity jurisdiction but they will power trip on it and take things as far as they can (at least on all my tours they were the ONLY authorities to give me any trouble. Cops, sherrifs etc. were nothing but helpful).

Also, if you do want to cut cross country, don't bother with a bike (at least not one you are attached to). You will wind up walking most the way.