A fan recorded the songs on her phone and later posted them to Instagram, along with a photo of herself with the I'll Show You singer, supposedly taken by Gomez.
The woman said she was having a drink at an "empty hotel bar" when the pair appeared out of nowhere.
She recalled the surreal experience of Bieber singing My Girl saying: "is this real? Pure magic."
They were later snapped stepping out, side by side, in LA.
The 21-year-old singer previously admitted the pair - who split in October last year - could get back together one day.
He said: "Maybe? We have a lot of history together and I am sure it could possibly happen.
"I think we are both just on our own journeys and figuring ourselves out and I think maybe once we figure ourselves out we can come back and make an awesome duo or she finds someone awesome and I'll find someone awesome. I just want her to be happy."
He went on to say she was someone, "I love dearly" and that would never change.
"I'm never going to stop loving her. I'm never going to stop checking in on her. I don't think if you end a relationship, you should end that, unless it was super toxic and you guys were hurting each other physically or mentally.
"We always respected each other and we still respect each other."
- Bang! Showbiz