February 03, 2013 12:50 PM

The key to surviving awards season? Being able to steal a moment of sleep anywhere and a good sense of humor.

In the past two weeks, Bradley Cooper, the Oscar-nominated star of Silver Linings Playbook, has flown from L.A. to Madrid to Paris to Rome to Manchester to Tokyo, L.A. again, New York, Washington D.C., New York and then finally L.A. (third time’s the charm).

But on the road, Cooper tells PEOPLE his most poignant stop this week was Thursday’s talk with military veterans at Walter Reed National Military Medical Center. It was the first time he has visited the hospital, but has traveled to deployed soldiers three times with the USO.

“A lot of vets have reached out saying they can really identify with Pat Solitano (his Silver Linings character). So we screened the movie last night – we thought 50 people would attend, and there were 200! We spent three hours there talking with them.”

“We made this movie knowing it was personal for [director] David [O. Russell], but it’s also become personal for so many people who have watched the movie.”

While he was in the air, the rumor mill kicked into high gear. Cooper quips, “It’s been quite a week. Apparently I’m shirtless while Soul Cycling and then high-flying after being heart-broken by a model who I send pictures of my feet, or she sends pictures of her feet to me. It’s just unbelievable.”

Cooper is referring to two separate reports, one that he ripped off his shirt after a SoulCycle class in Manhattan, causing a frenzy among cyclers. At the same time, word spread that he was allegedly dumped by model Laura Simpson because he was obsessed with her feet.

The truth? “The two things that are true about that are: I love Soul Cycle. But I would smack a guy if he took his shirt off at the end and then ran around saying, ‘Get after it.'”

And then the girl he did not date: “She is a friend of Jen’s (Lawrence, costar and fellow Oscar nominee) and we’d done the app Draw Something. We did a couple of Draw Somethings, a half a year ago, that’s it.”

So, did they draw any feet? He laughs, responding, “We’ll, only if BIGFOOT was a clue.”

With three more weeks until the Oscars, Cooper is just focused on enjoying the ride, adding, “It just gets crazier and crazier.”

Cooper (right) visits with James Pierce (center) and Jarred Lemon at Walter Reed

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