Justice Sangita Dhingra Sehgal extended the relief after the convict informed the court that the bail granted to him by the trial court is expiring on August 14.
Bhasin sought extension of the relief, saying he has also challenged the orders of conviction and sentence awarded to him by the sessions court in on July 15.
Accepting his contention, the judge said, "I extend the bail till August 23," adding that the bail bond will remain the same as imposed by the trial court.
The court, meanwhile, asked senior advocate Sidharth Luthra, appearing for Bhasin, to direct his client to give the compensation amount to the victims and sought their presence before it on the next date of hearing.
The trial court had directed the convict to pay a compensation of Rs 10 lakh to the deceased victim's kin and Rs 2 lakh to the other injured man, a journalist, who was riding pillion on a two-wheeler.
The sessions court had on July 15 sent Bhasin to jail for two years, for mowing down the motorcyclist with his over-speeding BMW car in 2008 while observing that cow killers get more stringent punishment than errant drivers.
"Sentence for killing cow is five or seven or 14 years in different states but in case of death of a human being caused by rash or negligent driving, sentence prescribed in law is only 2 years," Additional Sessions Judge Sanjeev Kumar had said.
The court had also granted him a statutory bail for enabling him to file an appeal in the high court and asked him to furnish a bail bond of Rs 50,000 with a surety of like amount.
The court had while convicting him dropped the charges of 304(II) (culpable homicide not amounting to murder) of the IPC.
Bhasin was driving his BMW car when he had hit the two-wheeler on Moolchand flyover in South Delhi, killing Anuj Singh on September 11, 2008. A TV channel journalist was also injured in the incident.