BLM rules and regulations for Wilderness Areas are codified under…
§ 6302.15 When and how may I collect or disturb natural resources such as rocks and plants in wilderness areas?
(a) You may remove or disturb natural resources for non-commercial purposes in wilderness areas, including prospecting, provided –
(1) You do it in a manner that preserves the wilderness environment, using no more than non-motorized hand tools and causing minimal surface disturbance; and
(i) Your proposed activity conforms to the applicable management plan; or
(ii) You have a BLM authorization if one is required by statute or regulation.
(b) Where BLM allows campfires in a wilderness, you may gather a reasonable amount of wood for use in your campfire.