The bus advert features topless men and women holding up the slogan "ride me all day for £3".
Celebrities including Charlotte Church, and Labour MP Jo Stevens are among those who have taken to Twitter expressing outrage at the company's advertising campaign.
The Everyday Sexism project, set up by Laura Bates in 2012, sparked further debates on Twitter, describing the advert as a "drop in the ocean".
The project highlighted a host of similar advertising campaigns devised by brands such as easyJet and SmartWater.
The social media backlash echoes the response to Protein World's controversial 'Beach Body' campaign.
NAT Group declined to be interviewed by PRWeek about the response to its campaign but, in a statement published on the company's website, it said it was trying to make the bus "attractive to the younger generation".
The statement continued: "While being a little tongue in cheek, it was in no way intended to cause offence to either men or women and, if the advert has done so, then we apologise unreservedly. There has certainly been no intention to objectify either men or women."