BLM land that you can use for camping is not "all over the place." Most of this category of public lands is in five southwestern states, and you are in the one that is crowded with people whi have diverse interests in the use of the lands.
Rules for use are different for different BLM properties. You need to do your homework before you go.
If you don't do the home work, and find yourself where you are not supposed to be, you might be asked to move. If you are not in a condition to make the move, the people doing enforcement may be inclined to move you to an internment facility, and your rig to an impoundment facility. Much depends on the attitude you display during the encounter.
If you do your homework, know the place you stay is a place you are permitted to stay, there will be no encounter. I use "permitted" in both general and specific sense. There are some places on BLM land where you need to buy a permit. Do your homework, make no general assumptions. It is all about specific places, specific times, specific uses; most users of public lands do it by permit or lease. "Camping" is one of the easiest uses, but don't assume you can do it just anywhere.