Acupuncture for Heroes and Seniors Act of 2019 This bill expands access to acupuncturist services, particularly for veterans and seniors. Specifically, the bill requires the provision of qualified acupuncturist services for veterans enrolled in the Department of Veterans Affairs (VA) health care system and military members and their dependents under the TRICARE program. A qualified acupuncturist is an individual who is licensed, certified, or otherwise accredited to perform acupuncture services. The bill also entitles military members and their dependents to qualified acupuncturist services under the TRICARE program without a referral, even if such services are not medically or psychologically necessary to prevent, diagnose, or treat an issue. The VA must implement a program to provide acupuncturist services in at least one VA facility in each Veterans Integrated Service Network in both urban and rural areas. Such services must be available to veterans enrolled in the VA health care system without the requirement of a referral. The VA must also establish the Advisory Committee on Acupuncturist Services to assist with the implementation of the VA acupuncturist program. The VA must pay acupuncturists equivalently with how it pays physicians. The bill provides for coverage for qualified acupuncturist services under the Medicare program and prescribes benefit amounts and payment rules depending on the circumstances of the service. The bill also makes acupuncturists eligible for appointment as (1) commissioned officers in the Armed Forces, and (2) officers in the commissioned Regular Corps and the Ready Reserve Corps of the Public Health Service.