Addressing the house after Deputy Chairman PJ Kurien gave her a second chance to speak, Ms Bachchan asked if the government had made any public apology to the victim's family.
"First of all, whatever happened? Did the government send any condolence to the family? Did you publicly make any announcement saying we are so sorry something so shameful happened in our country?" Ms Bachchan, a veteran film star, asked in Rajya Sabha.
"Sir, I'm basically an artist and I'm very, very disturbed by it. What is going to happen to her? Everybody will forget but she will remember for the rest of her life. It will be a scar. It's a terrible mental torture. How are you going to repay for this?" she said, her voice choking with emotions.
She then paused to wipe away her tears.
"Every day, women are getting raped by their fathers, their brothers, their uncles and it's a shame. We are bringing in bills for certain sections of society which are deprived. What about women who bring you into this world? Where is their protection."
"I'm ashamed. I personally feel very, very ashamed that I am sitting in this house and not being able to do anything and I am equally disturbed by the answers that keep coming to this house which are totally incorrect," she said.
She urged the government to amend Section 307 of the Indian Penal Code and make rape a crime at par with attempt to murder.
Ms Bachchan earlier had a spat with the chair when she was not allowed to speak beyond the fixed time limit.
She insisted the issue was important and she would protest by standing at her seat.
She was later allowed to speak again by the chair, making an exception.
"It is a shame. I don't know what all to say. I'm shaken," she said earlier.
"So far, I thought we are living in a country where women are considered idols and worshiped. We worship Durga, saying she is the goddess of power. All these ideals have been spoiled because every day, in cities of India, specially Delhi, such incidents occur," she said.