The 23-year-old medical student has been left fighting for her life after the attack, in which she was gang-raped by at least four men, brutally bashed, and then thrown out of the bus while it was still moving.
The driver of the bus and three other men have been arrested.
The rape has sparked widespread anger in India, with protests in New Delhi and other major cities including Mumbai, Kolkata and Ahmedabad.
Police used water cannon on one group of demonstrators as they tried to tear down steel barricades outside the official residence of Delhi's chief minister Sheila Dikshit.
Before the violence broke out, protesters carrying banners chanted: "We want equal rights for women."
Crowds also blockaded the headquarters of the city's police, while others, including opposition MPs, demonstrated outside parliament, urging the introduction of the death penalty for rapists.
"Women don't feel safe in the city, this is appalling," 18-year-old student protester Jayesha Koushik said.
"The blame is always put on the women. 'She was not wearing the right dress, she was out at the wrong time, she must have provoked it'. How can you blame the women for rape?"
Indian prime minister Manmohan Singh joined his ruling Congress party chief Sonia Gandhi in condemning Sunday night's "heinous" assault.
Mr Singh said he had asked Home Minister Sushilkumar Shinde to "ensure that (the) culprits are brought to justice and such cases do not recur", according to the Press Trust of India.
Mr Shinde announced in parliament that there would be a crackdown on buses having tinted glass and heavy curtains -- measures that should already be in force.
Even Bollywood superstar Amitabh Bachchan weighed in by calling on his Facebook page for "every Indian (to) become a vigilante, a soldier, a commander" to "fight such heinous crimes with strength and conviction".
The rape took place over a period of more than 40 minutes on Sunday in a bus which had stopped to pick up the woman and her male companion, who had spent the evening at a cinema.
"They began molesting the girl and her companion bravely fought back trying to save her but these men attacked him with an iron rod," police commissioner Neeraj Kumar said.
"The victim was dragged to the rear of the bus and brutally beaten and raped."
Three of the suspects appeared before a city magistrate on Wednesday where a police request for a custody extension was granted.
It is estimated a woman is raped every 20 minutes in India.