Reducing Administrative Costs and Burdens in Health Care Act of 2020 This bill requires the Department of Health and Human Services (HHS) to take a series of actions relating to health care administrative costs. Specifically, HHS must develop a strategy and take associated action to reduce unnecessary costs and administrative burdens in the health care system, including Medicare, Medicaid, and the private health-insurance market, by at least half over a period of 10 years. HHS must also award grants so that states may establish commissions targeting such costs.