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The New York Post reported that the bride was spotted wearing a diamond engagement ring with a round center stone and hopped into a hansom carriage after leaving the museum arm-in-arm.
"David told Lauren that he was taking her to see an exhibit, then got down on one knee. He had a beautiful ring ready. It was a total surprise to her, and they are both so happy," a source told the paper.
The bride is the niece of former president George W. Bush and granddaughter of former president George H.W. Bush. Her father is Neil Bush.
A former model, Lauren launched clothing line Lauren Pierce in 2009 and has helped feed more than 60 million impoverished children through the sale of her Feed Projects line of burlap bags. The groom is the executive vice president in charge of worldwide branding, communications and marketing at Polo Ralph Lauren.
A wedding date has yet to be set.