I now have a completely different perspective on the Woodrow Wilson Bridge. Crossing the WW on bike (or foot) is a whole different experience, lemme tell ya. The WW trail offers an amazing view of the river, Alexandria, and DC beyond. It's breezy up there and is a special view that you can't get any other way (well, by helicopter I guess). Free telescopes and benches make for pleasant stopping points and markers along the way offer interesting information and history.
We biked from Arlington, through Old Town, across the WW, all the way to National Harbor for an al fresco lunch. I never thought I'd be able to bike across the WW -- it just always seemed like an impenetrable force. It turns out to be quite friendly! Give it a try -- it's a million-dollar-view.