After much ado I finally got an answer from BLM. Here is a cut and paste of the document they sent me:
Recreational use of UAS on Public (BLM) lands – 8/21/17
There is no specific BLM restriction for flying UAS (drones) for recreational purposes on most public lands.
Local offices may have restrictions pertaining to flights in Wilderness/Wilderness Study Areas (WSA). Recreational UAS users are encouraged to consult the local office prior to flying on public lands.
Additionally, there may be Temporary Flight Restrictions (TFR) due to emergency responses such as wildfire. Recreational UAS users must remain clear of these areas and NOT interfere with fire management or emergency operations. If you notice a wildfire nearby, the best thing you can do is keep your UAS on the ground and find another location to fly. UAS can cause serious aviation accidents, which can be fatal.
Recreational use of UAS falls under the FAA Special Rule for Model Aircraft. The following FAA guidelines apply:
Fly at or below 400 feet
Be aware of airspace requirements and restrictions
Stay away from surrounding obstacles
Keep your UAS within sight
Never fly near other aircraft, especially near airports
Never fly over groups of people
Never fly over stadiums or sports events
Never fly near emergency response efforts such as fires
Never fly under the influence of drugs or alcohol
Model aircraft operators must follow these FAA rules to fly under the FAA Special Rule for Model Aircraft:
The aircraft is flown strictly for hobby or recreational use
The aircraft is operated in accordance with a community-based set of safety guidelines and within the programming of a nationwide community-based organization
The aircraft is limited to not more than 55 pounds unless otherwise certified through a design, construction, inspection, flight test, and operational safety program administered by a community-based organization
The aircraft is operated in a manner that does not interfere with and gives way to any manned aircraft
When flown within 5 miles of an airport, the operator of the aircraft provides the airport operator and the airport air traffic control tower (when an air traffic facility is located at the airport) with prior notice of the operation (model aircraft operators flying from a permanent location within 5 miles of an airport should establish a mutually-agreed upon operating procedure with the airport operator and the airport air traffic control tower [when an air traffic facility is located at the airport])
A model aircraft is defined as an unmanned aircraft that:
Is capable of sustained flight in the atmosphere
Is flown within visual line of sight of the person operating the aircraft
Is flown for hobby or recreational purposes.