Additional sessions judge P V Bavkar while rejecting the application granted time till March 16 to Doshi to approach the Bombay High Court for relief.
Additional public prosecutor R V Kini argued before the court that the allegations against Doshi, producer of films like the Amitabh Bachchan starrer 'Aankhen', were serious due to which he should not be granted anticipatory bail.
He pointed out that Saini had sustained injuries to her face and jaw which were serious in nature and that Doshi, if allowed to roam free, could affect investigations in the case.
Saini, has accused Doshi of having assaulted her on February 14 and subsequently threatening her after she filed a complaint with the police.
She has also accused Doshi of having raped her after promising her marriage, the proseuction said.
"There are two friends of Doshi, both of whom were witness to the incident on February 14 and they are unable to come forward due to Doshi being free," Kini told the court.
He added that there had been similar allegations levelled against Doshi in the past by his estranged wife which showed that he was a habitual offender.