Wyoming Public Lands Initiative Act of 2021 This bill designates specified wilderness study areas, special management areas, a National Conservation Area, and other areas in Wyoming. The bill designates the following areas as wilderness and as components of the National Wilderness Preservation System: certain land within the Encampment River Canyon Wilderness Study Area, to be known as the Encampment River Canyon Wilderness; certain land within the Prospect Mountain Wilderness Study Area, to be known as the Prospect Mountain Wilderness; certain land within the Sweetwater Canyon Wilderness Study Area, to be known as the Upper Sweetwater Canyon Wilderness and the Lower Sweetwater Canyon Wilderness; and certain land within the Bobcat Draw Wilderness Study Area, to be known as the Bobcat Draw Wilderness. The bill designates the following special management areas: Bennett Mountains, Black Cat, Sweetwater Rocks, and Cedar Mountain. The Bureau of Land Management shall divide the land within the Dubois Badlands Wilderness Study Area into the Dubois Motorized Recreation Area and the Dubois Badlands National Conservation Area, separating the two with a fence. The bill designates Fortification Creek, Fraker Mountain, and North Fork as management areas.