Uma Thurman, 37, is rumored to be engaged to her new boyfriend, Swiss millionaire investment banker Arpad Busson, 44. He was said to have proposed in early October after just a few months of dating, but if that’s true he either didn’t give her a ring or she’s not wearing it out. She has been seen out since, including her infamous appearance at Fashion Rocks in a see-through dress, and she isn’t wearing an engagement ring.

Now Star reports that Uma has asked Arpad to move in with her in NY. He is said to have a home base out of London, so maybe it would be more convenient for her if he’s staying with her while he’s in NY:

After just three months of dating, Uma Thurman has asked multimillionaire financier Arpad Busson to move into her swanky NYC apartment! “Uma likes having Arpad at her side,” explains a friend, noting that Uma and hotelier Andre Balazs broke up “because he always had to work. She doesn’t like being by herself” But Arpad, the father of supermodel Elle Macpherson’s two children, “makes time for her.”

[From Star Magazine, print edition, October 29, 2007]

That’s the entire story, so maybe Star is just making it up because there aren’t a lot of details there.

One recent story about Uma that might be true is the claim that she insists on doing her own hair and makeup when she’s on a movie set and refuses professional help. Whitney Bears does that too, but they make it sound like Uma is less stubborn about it and just doesn’t want people fussing over her:

An insider tells Star that whenever Uma works on a movie, she insists on doing her own makeup and styling. In fact, when she starred in the 2005 film Prime, she wore clothes from her own closet. “Uma doesn’t like a lot of fuss,” says the insider, especially when it comes to makeup. “The stylists would try to sneak in touch-ups, and she’d shoo them away.”

[From Star Magazine, print edition, October 29, 2007]

Whatever Uma is doing lately, it’s working. She looked positively gorgeous at Fashion Rocks in that gauzy dress that left little to the imagination. Maybe her new romance is giving her a natural glow too.

Uma and Arpad are shown at Petra Nemcova’s Happy Hearts Fund Heart of Gold Ball on 10/11/07. Thanks to Splash News.