The actress appeared with Daggubatti in the crime thriller Dum Maaro Dum.
A source told The Times of India: "Bipasha didn't want to come without an escort, as she knew that her former flames Shahid [Kapoor] and John Abraham would also be there... so she brought Rana.
"She and Rana became friendly after working together in Dum Maaro Dum and have grown close since."
The insider continued: "[Daggubatti] flew into Mumbai on November 5 at noon and checked into a suburban five-star hotel. Later that evening, he arrived at the party with Bipasha and her posse of friends.
"Rana returned to Hyderabad on an early morning flight the next day to resume work."
The two stars were rumoured to be dating following Basu's breakup with her long-term boyfriend John Abraham.
In October, the actress tweeted that media reports about plans to marry Daggubatti were entirely false.
Watch a trailer for Dum Maaro Dum below: