It's a hard one to answer.. if you say what she said then you risk being outed as someone who wouldn't share the $$$ and thus they won't pick you to go over the bridge. But if no one says anything, who ever is selected might keep it for themselves. So you need to have the discussion to sound out who is the best choice to send across.. & try as hard as you can to get them to choose you..
Like you said $250K isn't life changing, but it certainly would give your lifestyle a kick along
I think I'd be inclined to lie to everyone and tell them I am a good choice... then take it for myself