Birth Access Benefiting Improved Essential Facility Services Act or the BABIES Act This bill requires the Centers for Medicare & Medicaid Services (CMS) to establish a Medicaid demonstration program to improve freestanding birth center services for women with low-risk pregnancies. Among other things, the CMS must (1) publish criteria for freestanding birth centers to participate in the program, including specified accreditation, licensure, and service requirements; (2) publish guidance for states to establish prospective payment systems under Medicaid for program participants; and (3) award planning grants for states to develop program proposals. The CMS may choose up to six states to participate in the program.