But the bigger goal, she says, is to put Delaware Bay on the map.
"We spend a lot of time talking about Delaware Bay as a place for fish and wildlife. A lot of people think of it as a place for ships and industry," said Jennifer Adkins, executive director of the nonprofit Partnership for the Delaware Estuary.
"What she's trying to highlight is that the bay is a place for people."
Attempts to boost the bay's cachet include a spring 2012 visit from then-Interior Secretary Ken Salazar, who praised it as "a landscape of national significance."
Nice plug, but no money. An analysis of federal funding for 2012 shows that the Great Lakes got $300 million. Chesapeake Bay got about $60 million. Delaware Bay ranked eighth, with just $700,000.
Wren called her attempt to cross the bay "almost inevitable."
She loves open-water swimming. She lives on the bay - at Cumberland County's Money Island - and her work is all about the bay. Now 48, she began to think about whether she had accomplished enough.
Plus, "I mentioned it to my dad, and he said, 'If you're going to do it, I'd like to see it, so do it soon.' "
Her primary logistics expert is her husband, Jesse Briggs, who is well acquainted with the whims of the bay and its weather. He's captain of the A.J. Meerwald, a 1928 oyster schooner that her center owns. It is New Jersey's official tall ship.
Why Saturday? It's not a full moon, which would heighten the tides and strengthen the bay's notorious currents.
Wren, who also does triathlons, has calculated her crossing based on a freestyle swimming speed of 1.8 miles an hour - less than a recent pace during a seven-mile swim, but that was in a pool.
Her route will take her beyond Deepwater Point, then across the shallows of Joe Flogger Shoal. All the while, the current will be pushing her upriver - north of what would otherwise be a straight shot across.
She hopes to reach the shipping channel at slack tide, before the current reverses and pushes her back south.
A dispatcher for the Pilots' Association for the Bay and River Delaware said Wednesday that three ships could cross her path. "We'll be in constant radio contact," Wren said. "Mostly, we have to stay out of their way."
After that, she will be swimming atop prime oyster beds. Given the oyster's historic and current significance on the bay, she said, "it feels good to have that be part of my journey."
Closer to Fortescue, the currents are less predictable. So the flotilla of kayakers and swimmers who plan to escort her in may have to adjust.
Wren said she chose Fortescue as her destination because it was heavily damaged last year in Hurricane Sandy and, unlike communities on the Atlantic Coast, is not getting significant rebuilding funds.
Plus, its public beach offers good access to the bay.
"I hope people will think of the bay as a place that they want to be associated with, a place they want to be in and around," Wren said. "It's a beautiful place."
For more information, go to http://swimdelawarebay.org or Swim Delaware Bay on Facebook.
Contact Sandy Bauers at 215-854-5147 or sbauers@ phillynews.com, or follow on Twitter @sbauers. Read her blog, "GreenSpace," at www.philly.com/greenspace.