I'll pile on with wait until you are close to decide. Yesterday they had announced they were going to open the Woodrow Wilson bridge over the Potomac at 2:30 in the afternoon. They later cancelled it because they decided the ship could make it underneath, but that would have made some issues for the eastern way. You just never know what will be going on!
As others have said it will depend. But worse is South of that on 95 between DC and Fredericksburg, especially crossing the Occoquan. If you can, I would budget for the hov lanes and take those Anywhere between $20-$40 but well worth the money.
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