Continuity of Business Operations Support Act of 2020 This bill requires the Small Business Administration (SBA) to provide grants to small business development centers, women's business centers, and chapters of the Service Corps of Retired Executives to educate and advise small businesses on specified matters related to COVID-19 (i.e., coronavirus disease 2019). The SBA must establish goals and metrics for the use of such funds awarded to small business development centers, which shall (1) consider the extent of the circumstances relating to the spread of COVID-19 that affect small businesses served by grant recipients, (2) ensure grant recipients have the flexibility to respond to unique situations, and (3) encourage grant recipients to develop and provide services to small businesses in areas substantially affected by COVID-19.