Advanced Safe Testing at Residence Telehealth Act of 2023 This bill temporarily establishes several programs to provide telehealth services for at-home testing, evaluations, and other health care. Specifically, the bill establishes a demonstration program to provide assistive telehealth consultations and home- and community-based care for certain Medicare beneficiaries through Medicare Advantage (MA) plans. Covered services include certain at-home diagnostic tests, telehealth consultations, transportation services, and meal benefits. Beneficiaries must be (1) age 65 or older and eligible to enroll in a qualifying MA plan and to receive certain low-income subsidies under the Medicare prescription drug benefit, or (2) dually eligible for Medicare and Medicaid benefits. The bill also establishes a grant program for state Medicaid programs to cover similar at-home tests and related telehealth consultations. Additionally, the Department of Veterans Affairs must establish a pilot program to provide tests and related telehealth consultations free of charge to veterans.