Bhonsle, who was attending the ceremony on Thursday, tweeted a photograph of herself with Irani.
Modi Swearing In ceremony: Bollywood celebs Kangana Ranaut, Karan Johar, Rajinikanth, Shahid Kapoor, Sushant Singh Rajput & others at Rashtrapati Bhawan
She captioned it: "I was stranded in the crazy rush post PM's oath ceremony. No one offered to help me except Smriti Irani, who saw my plight and made sure I reached home safely. She cares and that is why she won."
The who's who of Indian business, cinema, politics and sports gathered to witness the event in the forecourt of the Rashtrapati Bhavan.