The 41-year-old actor will be making his directorial debut with the upcoming "A Star Is Born" and the duo are bonding by doing everyday tasks together, reported Grazia magazine.
"It's a huge project for Bradley and he wants to build momentum. He's hanging out with Gaga a lot to get in the zone.
"He's been at her house and they've been doing bonding exercises, such as having brunch and going shopping. They share a love of vintage cars too and they're getting on like a house on fire," a source said.