Vinay Sharma had moved the bail application saying he was a BA first year student and that incarceration was affecting his studies.
Special Public Prosecutor Dayan Krishnan, opposing the bail plea, said Sharma may jump the bail and tamper with the evidence.
In its reply filed before Additional Sessions Judge Yogesh Khanna, police said Sharma will have enough time to study in judicial custody.
"In view of the above facts, the bail application of Vinay is strongly opposed as the main prosecution witnesses are yet to be examined and if bail is granted, he may jump the bail and tamper with evidence."
Vinay, in his bail plea, also said that he has to attend his ailing mother in a hospital.
In response, the prosecution said that Vinay's mother is not hospitalized and was found in her house and "therefore, it is requested that the bail application of Vinay may kindly be dismissed for the sake of justice".
Vinay's counsel A K Singh also informed the court that his client had applied for a post in the air force, for which he had cleared the written exam and now he has to appear for interview on April 5, so he be granted bail.
Earlier during the hearing, Mukesh, another accused was taken to Safdarjung Hospital after he complained of chest pain, leading to the day's court hearing being adjourned for an hour. He was produced before the court at 3 pm after doctors discharged him, attributing his pain to gastric discomfort.
All the four accused - Mukesh, Vinay Sharma, Pawan Gupta and Akshay Thakur - were brought to the court, guarded by 15 policeman.
Meanwhile, Mukesh's counsel M L Sharma also moved an application before the court for complete medical check-up of Mukesh and Akshay daily by the jail doctors.
He created ruckus in the court room, saying he need to cross examine all the 52 witnesses again as his clients did not what is going on in the trial. However, the court objected, saying: "Don't delay the trial".
He also sought permission to visit Mukesh in hospital. "One (brother) has died and another is in hospital. Something is fishy. I am worried about the health of Mukesh, allow me to visit him in hospital." The court rejected his demand.
The advocate said that his clients were not provided copies of the charge sheet in Hindi and were even not aware of their charges against them. Denying his charges, Krishnan said a Hindi copy of the charge sheet has been provided and it is on record.
During the hearing, Sharma went over to Vinay Sharma and Pawan Kumar and asked them if they understood the proceedings. When they replied yes, he shouted: "You are going to be hanged", leading to objections from their counsel.
He also refused to cross-examine witnesses saying he needed a day before cross-examinations. The court and prosecution again objected to the "delay" tactics.
Sharma had replaced V K Anand, who was earlier appearing for Ram Singh and his brother Mukesh, after the former was found dead in jail, having allegedly committed suicide.
Only one witness was cross-examined Monday by Vinay and Pawan's counsel.
The fast track court started day-to-day trial in the case after it framed charges of murder, gang-rape and kidnapping, among others, under various sections of the Indian Penal Code (IPC) against five of the six accused.
Proceedings against Ram Singh abated after his death earlier this month, and the case of the sixth accused, a minor, is being heard by the Juvenile Justice Board.
The 23-year-old trainee physiotherapist who was brutally raped by the six accused in a moving bus on Dec 16 had died Dec 29 in a Singapore hospital.