The actress – who plays lesbian Muslim Rhana Habeeb in the ITV soap – told producers: “I’m full Asian!”
She said the bizarre rejection for being “too pale” was a sign she would have to “work a little bit harder” than white actors to achieve success.
Though she had found it a “difficult pill to swallow” Bhavna, 34, said pursuing a career as an actress was “still worth doing”.
The star – whose mum is Indian and dad from Kenya – also played Alia in hit BBC comedy Citizen Khan.
She told Manchester-based A-Magazine before turning to acting she used to work as a costume designer where her looks were unimportant.
“With costume it’s about how good you are, how creative you are,” she said.
“With acting it was, `You’re too tall. You’re too short. You’re too fat. You’re too thin’.
“I once went to a job and was told I was too pale to play an Asian character and I said, `I’m full Asian!’.”
She realised “certain things in the industry weren’t as easily in reach for me as they were for a Caucasian actor”.
But it made her more determined to succeed.
“If you’ve got a platform to try and make a difference then you should use that platform,” she said.
“If it means you have to work a little bit harder than other people may have to it’s still worth doing.”
Bhavna said playing Rhana – who in the soap is planning to have a baby with her lover – was “one of my biggest challenges but also one of my biggest achievements”.
“Having the platform on Coronation Street and having the opportunity with this storyline means so much to me,” she said.
“I did a lot of research and put my heart and soul into it.
“The thing that’s probably helped is pushing myself to do things that scare me, staying true to myself and having a lot of respect for the people around me.”
She and Corrie co-star Faye Brooks, 31, who plays her TV lover Kate Connor, were nominated for Best On-Screen Partnership at the British Soap Awards.
And Bhavna earned a Best Actress nomination at the TV Choice Awards.
But she does not think she has made it.
“I think I still have a long way to go,’’she said.
“I know in America it’s changing – there’s a lot of colour-blind casting.
“But in the UK we’re slightly behind.
“A lot of people are doing good work and a lot of the girls I used to audition with are now flying high.
“But I know there’s still a few barriers that we have to overcome.”