The bridge is the only safe passage from Anbar to Baghdad province for thousands of displaced people trying to flee fighting in the area over the past few days. It was closed on Friday.
Officials did not give CNN a clear answer as to why it was shut down.
"ISIS from that side and from here the road is blocked," said Sabah Hamid, a woman fleeing ISIS. "Where are we supposed to go?"
Iraqi security officials said that ISIS took control of Husayba -- a small town about 11 miles (17 kilometers) east of Ramadi and about 14 miles (22 kilometers) west of Habbaniya -- in an assault that involved car bombs and heavy machine gun fire.
It's the terror group's latest push east since it seized the key city of Ramadi
, a milestone that a U.S. State Department official acknowledged is a major blow
in coalition efforts to defeat ISIS.
Witnesses said the militants summarily executed people in the street whom they accused of working with the government.
"They were killing anyone who they accused of being with the police or the army," one witness told CNN.
About 25,000 people have fled Ramadi, with most of them headed to Baghdad, the United Nations said.
The militants now appear to be heading towards al Khalidiya, the last town between Ramadi and Habbaniya's military base and airbase.
Habbaniya base has been designated a staging point for Iraqi security forces and Shiite militias in their attempt to retake Ramadi and the rest of Anbar province.
In recent days, thousands of people have crossed the Bzebiz Bridge, hoping that they'll be safer in Baghdad.
Normally there are security procedures in place for the bridge -- the Iraqi government requires that anyone who is not from Baghdad and is trying to enter the area from Anbar must have a sponsor in Baghdad. There are reports that the restrictions have been sporadically lifted over the past few days.
Now though, those who are stuck in Anbar are fearful of ISIS and furious at their government.
One man told CNN that he was so upset that if he died, he didn't want to be buried in Iraq. He said he cannot consider a country that treats him as such to be his own.
Four years of war
broke out four years ago in Syria, providing an opening for groups such as ISIS to emerge and take on forces loyal to Syrian President Bashar al-Assad
. With its latest offensive, ISIS controls more than half the country -- in parts of 10 of 14 provinces -- as well as "the vast majority of the gas and oil fields," the observatory estimates.
Thursday it took over the last Syria-Iraq border crossing that was under the control of Syrian troops, the Syrian Observatory for Human Rights said. The Tunef border crossing fell under ISIS control after Syrian regime troops withdrew, the activist group reported. ISIS also controls the Al Waleed border station on the Iraqi side.
In western Syria, Islamist rebels with Jabhat al-Nusra seized the National Hospital on the southwest outskirts of the city of Jisr Ash-Shughur from al-Assad forces, according to the group.
Also under threat is the ancient Syrian city of Palmyra, where ISIS forces have expanded their control in recent days.
The jihadist rebels took a military station in the countryside as forces loyal to al-Assad
abandoned the site overnight, the Syrian Observatory for Human Rights reported Friday.
Some 11,000 people have fled the city and its surrounding villages following ISIS taking control of the area this week, the U.N. Refugee Agency said.
About 8,000 have gone to the village of Al-Qarayateen, some 40 miles southwest of Palmyra, while another 3,000 fled to Furglus, a village 20 miles east of Homs, the UNHCR said in a statement.
"People are arriving exhausted, scared and in increasing numbers," said Bhajat Al Arandas, an official with the Al-Birr Society, which partners with the UNHCR. "They fled their homes in Palmyra and neighboring villages with hardly anything and report there is no water, electricity or working mobile phone network (in Palmyra)."
Palmyra, about 150 miles northeast of Damascus, is a UNESCO World Heritage Site described as having "stood at the crossroads of several civilizations," with its art and architecture mixing Greek, Roman and Persian influences, according to that U.N. group
This week's fall of Palmyra spurred condemnation worldwide, leading to tweets that used #SavePalmyra.
"The ruins are absolutely glorious," said CNN iReport contributor Aradhana Anand
, who visited Palmyra in 2010. It's "heartbreaking, really."
British historian and novelist Tom Holland has described Palmyra as "an extraordinary fusion of classical and Iranian influences intermixed with various Arab influence as well."
Extensive destruction of Palmyra wouldn't just be a tragedy for Syria. It would be a loss for the world, Holland said.
"Mesopotamia, Iraq, Syria, this is the wellspring of global civilization," he said. "It really couldn't be higher stakes in terms of conservation."
U.N. and Syrian officials have expressed fears that ISIS will destroy the ruins, just as it flattened the ancient Assyrian city of Nimrud and smashed statues in Iraq's Mosul Museum.
Historian: 'Couldn't be higher stakes'
ISIS is "distinctive and horrendous" in how it treats history, Holland said. Syrian antiquities chief Maamoun Abdulkarim said the group poses "the biggest danger" now to his country's artifacts.
"In general, ISIS attacks people first for control," Abdulkarim said. "Second, they attack heritage by destroying for propaganda and ideological reasons. And (third), they work with the mafia to sell the artifacts."
The Syrian government says it has moved many artifacts, including hundreds of statues, to safer locations. But it can't relocate an entire archaeological site.
"We consider this ... a culture battle for humanity and all the world," Abdulkarim said. "Palmyra is very important in the minds of the Syrian people and also the international community. Now we are very afraid."