The 39-year-old actor was spotted winning the bear for the 32-year-old actress while being directed by Clint Eastwood.
Last week, Bradley and Sienna were seen chatting during a break from filming.
It was recently announced that Bradley and Clint will be presenters at the 2014 Tony Awards, which is airing Sunday, June 8.
15+ pictures inside of Bradley Cooper and Sienna Miller filming American Sniper… More Here! »