The actor - who split from Zoe Saldana for the second time last year - and the blonde beauty were spotted enjoying a day out in the Massachusetts city on Monday (18.03.13) after he paid to fly her out to the set of his new film, an as-yet untitled David O. Russell/Abscam project.
Bradley, 38, met the British model, who is 18 years his junior, at the ELLE Style Awards in London last month and although the pair are taking things slowly, he is said to ''really'' like her.
A source told Us Weekly: ''It's new but they're hanging out. He's really into her.''
A source previously said: ''Bradley has been texting Suki every day since they met ... Suki had so much fun with Bradley when he was in the UK.
Bradley recently admitted he is on the lookout for a new girlfriend and would like to find a woman who is a ''free spirit'' who can make his heart race.
He said: ''I look for a girl that is fun, a free spirit. I'm a romantic. I can be soppy.''