The 32-year-old singer bonded with her 'A Star is Born' co-star over a pasta dinner and her piano and she knew straight away there was ''no other'' person who could have made the movie than the 43-year-old actor.
She recalled to 'Entertainment Tonight': ''I actually was performing at a cancer fundraiser for Sean Parker and I sang the song 'La Vie En Rose,' which, not to give it away, but it is in the film, and I sang that song, and the very next day, he wanted to meet me and he came over to my home.
''I opened the door, and the second I looked into his eyes I felt an instant connection to him.
''We're both from the east coast, we're both coming from Italian families, I was like 'Are you hungry?' I cooked him up some leftover pasta, and we were eating, and before I knew it, he said 'I would like to sing with you, if that's OK.'
''And we went to the piano, and I printed out the sheet music for a song that he wanted to sing called 'Midnight Special.' ''
Gaga admitted she wasn't prepared for how ''incredible'' Bradley's singing voice was.
She added: ''I sat down and started to play, and he began to sing and I just stopped instantly in my tracks, and I looked at him and I said, 'Bradley, you have an incredible voice, you sing from your gut, you sing from your soul, you sing from the nectar of your being.'
''He said, 'Should we film it?' So he filmed it on his iPhone, and we all of a sudden started to sing together, harmonising and laughing, and looking at each other.
''It was instantaneous, and I knew in this moment that I could make this film with him, and I truly believe that there's no other actor or director in the world that could have played this role or made this film.
''There's no other actor that could play a rock star, he's the only one.''
And the 'Poker Face' hitmaker thinks Bradley would be successful if he decided to pursue a singing career.
She insisted: ''If he wants to, he can do anything.''
The 'Silver Linings Playbook' actor agreed their meeting was ''magical''.
He said: ''I remember every single moment of it. From the moment she walked down the stairs, it was one of those magical things.''