Demonstrators also occupied a tall building overlooking the bridge, taking new ground in the center of the Iraqi capital after protests had appeared to lose momentum.
A bomb blast at a nearby square during the night killed at least three people, police and medics said, but it was not immediately clear who was responsible or whether it was linked to demonstrations.
More than 300 people have been killed during weeks of mass unrest in Baghdad and southern Iraq.
Protests that began in October over lack of jobs and public services have swelled. Demonstrators are now demanding the departure of Iraq’s ruling class and an overhaul of the governance system that has fueled corruption since the toppling of Saddam Hussein in a U.S.-led invasion in 2003.