Victim Meher Jaan Mohammed Lamberaj, working as a manager in a private firm, left home in Tardeo area at about 4 AM for morning walk and reached Air India junction in Marine Drive at 5.45 AM when the thief and his aide struck her.
She sustained minor injuries but is out of danger.
While she was walking on a footpath hearing music from her mobile using earphones, one of the two accused tried to snatch it but she resisted before raising an alarm, police said.
As other morning walkers rushed to the victim's rescue, the accused escaped on the bike, police said adding that the woman was taken to a nearby hospital with minor injuries.
The two accused were booked under relevant IPC sections and the CCTVs installed in the area were being sought to see if the incident was captured, police said.