Onlookers said Ecclestone "seemed very excited" to see the car, which was a gift from her mother Slavica, a former Armani model, parked outside their hotel in Beverly Hills.
She and Stunt are staying at a hotel while they wait to move into Aaron and Candy Spelling's former home in Los Angeles, which Ecclestone purchased in July.
"Petra and her husband James are very excited to be moving to L.A.," a source tells PEOPLE. "They're staying in a hotel until renovations on their new home are complete, but they hope to move in later this month."
Ecclestone also plans to attend New York's Fashion Week later this month to present her new Stark handbag line, according to the source.
Reporting by PERNILLA CEDENHEIM