Bandelier National Park and Preserve Establishment Act This bill converts the Bandelier National Monument in Sandoval County, New Mexico, into a unit of the National Park System known as the Bandelier National Park and Preserve. The Department of the Interior shall permit hunting on land in the preserve in the same manner as hunting is managed in the Valles Caldera National Preserve. Interior shall provide access to traditional cultural and religious sites in the park and preserve by members of Indian tribes for traditional cultural and customary uses. Interior shall allow an enrolled member of any tribe that is culturally affiliated with the land within the park and preserve or the Valles Caldera National Preserve to collect plants and mineral resources for noncommercial traditional and cultural uses. Interior shall establish a tribal commission for the park and preserve to provide guidance and recommendations on the development and implementation of management plans for and policies of the park and preserve. Interior and the Department of Agriculture shall seek to enter into an agreement to adjust the boundary between the Valles Caldera National Preserve and the Santa Fe National Forest to improve management of those areas.