Domestic help Deepali Mane had alerted the driver after Varsha, who was alone in the house, did not answer the doorbell. The driver entered the flat through Bhosle's elder sister and singer Lata Mangeshkar’s adjacent house.
No suicide note was found, the police said, adding that she shot herself in a Belgian-made pistol.
Varsha, who sang for some Hindi and Marathi films besides appearing in concerts with her mother, reportedly tried to end her life in 1998 and 2008.
She was the second of Bhosle's three children with first husband Ganpatrao Bhosle. Varsha, who also wrote for magazine and web portals, had married sports writer and public relations professional Hemant Kenkre, but the couple divorced in 1998.
Varsha Bhosle had written for a wide range of publications, including the Sunday Observer, the now-defunct Gentleman magazine and occasionally for The Times of India in the past.
A political science graduate from Elphinstone College, she frequently wrote for rediff.com, where she penned numerous columns on political and current affairs.
Asha Bhosle, who was in Singapore to attend the closing ceremony of the Marathi International Film and Theatre Awards (MIFTA), rushed back to India.
The body has been taken to J.J. Hospital, where a post-mortem was conducted late in the evening, said sources in the hospital.
Varsha shot herself with my old, lost gun: Says Asha Bhosle to Police
Speaking to the police at her Peddar Road apartment, the grieving Asha Bhosle said that the pistol used by her daughter was registered under her name, that she had misplaced it, and had no idea how Varsha found it
Legendary singer Asha Bhosle confirmed that her daughter Varsha, who shot herself in the head in the wee hours on Monday, was a patient of depression and had made herself virtually invisible from public life for a year.
Bereaved: Asha Bhosle arrived at her residence from Singapore on Monday around 10 pm. Soon after that her family performed the last rites.
Asha Bhosle also put an end to the mystery surrounding the ownership of the pistol used by the 56-year-old columnist to shoot herself. The singer revealed that she was the owner of the weapon, and had earlier misplaced it.
A team of police officials from Gamdevi police station visited Asha's Prabhu Kunj building at Pedder Road on Tuesday, and as a part of the investigation, had a brief conversation with her.
"Varsha was depressed owing to her loneliness and she had also distanced herself from everyone in the past one year. Varsha was being treated for depression, acute pain in her leg and diabetes. Lately, she seemed disconnected from the outside world. She had even stopped using her cell phone," Asha Bhosle told the police team.
The police revealed that Asha had returned from Singapore on Monday around 10 pm, and soon after that her family performed the last rites at the Chandanwadi crematorium in Marine Lines.
"Asha Bhosle was inconsolable. Hence her lawyer, who was present at the residence, asked us to wait for her son's arrival before starting the process of recording statements," said an inspector from Gamdevi police station.
Though cops only managed to have a brief conversation with Asha, she told them that the weapon used by her daughter to commit suicide actually belongs to her.
"The pistol that Varsha used to shoot herself is registered in my name. It is very old and it had been lost. We don't know how Varsha got her hands on it," she said.
Sources revealed that there are two other guns in the family: Asha Bhosle's brother Hridaynath Mangeshkar owns a .32 pistol, while her son Anand owns a .45 pistol.
Varsha Bhosle had used a Belgian make Baby Browning, which she placed against her left temple and pulled the trigger early on Monday.
Police said that they would be recording a formal statement from Asha Bhosle very soon. They are also awaiting the return of Asha Bhosle's son from Singapore.