The campground is two miles in from the entrance of the park. There are metro stations you can drive to. There was a .7 mile trial from the back of d loop to a metro station but it’s closed. You can take Lyft/Uber, we used the ranger station near b loop and it was about $25-30 each way and about 30 mins.

Yes, there are Metro stations nearby. The Park office has maps and information on DC.