Broadband Reform and Investment to Drive Growth in the Economy Act of 2021 or the BRIDGE Act This bill establishes and provides funding for the Broadband Access Fund and makes other changes related to expanding access to broadband services. Specifically, the National Telecommunications and Information Administration must use the funding to award grants to states, territories, and Indian tribes for deploying, increasing adoption of, and facilitating affordable access to broadband and promoting digital equity (i.e., the condition in which all individuals and communities have the information technology capacity needed to participate in the society and economy of the United States). Grantees must prioritize deployment of broadband in unserved areas (including high-cost areas) and activities in areas with poverty rates above the national average. The bill also preempts state and local laws that prohibit a public telecommunications provider (e.g., a municipal broadband provider) from offering broadband or other telecommunication services or deploying a network or infrastructure necessary for such services. Additionally, the Federal Communications Commission must report on improving its effectiveness in achieving universal service goals for broadband.