It's a 10-15 minute drive up 395 from DCA to the ballpark.
You could take the water taxi from Old Town Alexandria to the ballpark, but that would involve both Metro and a bus ride between DCA and Old Town, and would probably take a lot longer than taking Metro alone. And Metro shouldn't take more than 20 minutes or so during the week. On the weekend, that's another story.
I have no car. There's no way Metro gets from DCA to Navy Yard in 20 minutes ...
