No direct bridge connects New Jersey to Brooklyn.
The Brooklyn Bridge spans the East River between Manhattan and Brooklyn. To drive from New Jersey to Brooklyn, you must cross the Hudson River into Manhattan first (via the George Washington Bridge, Lincoln Tunnel, or Holland Tunnel), then take the Brooklyn Bridge or another East River crossing (Manhattan Bridge, Williamsburg Bridge, Battery Tunnel).
Alternatively, the Verrazzano‑Narrows Bridge connects Brooklyn to Staten Island, and the Goethals Bridge / Outerbridge Crossing link Staten Island to New Jersey—a longer route.