is there parking at the museum of the bible?

Street and garage parking.

There are parking garages in some of the office buildings nearby but they do fill up and are not cheap

Not sure. If there is one very hard to get spot. Always busy and heavy traffic in that area.

There is also a Metro right around the corner from the building

There is a parking area nearby but it does not have its own. There are a few spots on the street nearby but tyey fill up fast. It is best to get a cab or uber to get there, or depending on how far you live/are staying it may be better to walk if it is not too far.